GIFT   OF 
Mrs.   Dwayne  Young 


The  Principles  Underlying 
Radio  Communication 


RADIO  PAMPHLET  No.  40 

December  10,  1918 

Signal  Corps,  U.  S.  Army 


Washington  :  Government  Printing  Office  :  1919 


U 


War  Department 

Office  of  the  Chief  Signal  Officer 
GIFT 


/;/ 


THE  PRINCIPLES  UNDERLYING  RADIO 
COMMUNICATION. 

Prepared  by  the  Bureau  of  Standards  under  the  direction  of 
the  Office  of  the  Chief  Signal  Officer  of  the  Army,  Training 
Section. 

Acknowledgment  is  made  of  the  Valuable  service  rendered  the 
Signal  Corps  by  the  Bureau  of  Standards  through  the  work  of 
Dr.  J.  H.  Dellinger  and  the  following  men  engaged  with  him  in 
the  writing  of  this  book: 

Dr.  F.  W.  Grover. 
Prof.  C.  M.  Smith. 
Prof.  G.  F.  Wittig. 
Dr.  A.  D.  Cole. 
Dr.  L.  P.  Wheeler. 
Prof.  H.  M.  Royal. 

3 


ADDITIONAL  COPIES 

OF  THIS  PUBLICATION  MAY  BE  PROCURED  FROM 
THE  SUPERINTENDENT  OF  DOCUMENTS 
GOVERNMENT  PRINTING  OFFICE 
WASHINGTON,  D.  C. 

AT 

55  CENTS   PER  COPY 

V 


PREFACE. 

In  this  book  are  presented  briefly  the  basic  facts 
and  principles  of  electromagnetism  and  their  applica- 
tion to  radio  communication.  In  the  effort  to  present 
these  topics  in  a  simple  manner  for  students  with  very 
little  mathematical  preparation,  it  has  been  necessary 
at  times  to  use  definitions,  illustrations,  and  analogies 
which  would  not  be  used  in  a  work  prepared  for  more 
advanced  students.  Frequent  references  to  standard 
books  are  given  for  further  study,  and  students  should 
be  encouraged,  as  far  as  possible,  to  consult  them. 

5 


TABLE  OF  CONTENTS. 

INTRODUCTION. 

Page. 

1.  What  radio  communication  means 15 

2.  Fundamental  ideas  of  electric  circuits 16 

Chapter  1.  Elementary  Electricity. 

A.  ELECTRIC  CURRENT. 

3.  Effects  of  electric  current 23 

4.  Magnitude  and  direction  of  current 24 

5.  Measurement  of  electric  current  and  quantity  of  elec- 

tricity   25 

6.  Electrons 26 

B.  RESISTANCE  AND  RESISTIVITY. 

7.  Resistance  and  conductance 27 

8.  Resistivity  and  conductivity 28 

9.  Temperature  coefficient 30 

10.  Current  control 31 

11.  Conducting  materials 32 

12.  Non-conducting  or  insulating  materials 34 

C.  POTENTIAL  DIFFERENCE,  EMF.,  AND  OHM'S  LAW. 

13.  The  meaning  of  emf 36 

14.  Ohm's  law 38 

15.  Sources  of  emf 42 

16.  Internal  voltage  drop  and  line  drop 46 

D.  BATTERIES. 

17.  Kinds  of  cells 49 

18.  Simple  primary  cell 49 

19.  Types  of  primary  cells 51 

20.  Dry  cells 52 

21.  Storage  cells 53 

22.  Internal  resistance  in  batteries 59 

7 


OF  CONTENTS. 
'E.  ELECTRIC  CIRCUITS. 


Page. 

23.  Current  flow  requires  a  complete  circuit CO 

24.  Series  and  parallel  connections 61 

25.  Divided  circuits.    The  shunt  law. 66 

26.  The  potentiometer- 67 

27.  The  Wheatstone  bridge 69 

28.  Heat  and  power  losses 70 

F.  CAPACITANCE. 

29.  Dielectric  current 71 

30.  Condensers 72 

31.  Dielectric  properties 74 

32.  Types  of  condensers 76 

33.  Electric   field   intensity 77 

34.  Energy  stored  in  a  condenser 78 

35.  Condensers  in  series  and  in  parallel 79 

G.  MAGNETISM. 

36.  Natural  magnets 81 

37.  Bar  magnets 81 

38.  The  magnetic  field 82 

39.  Magnetic  flux  and  flux  density 83 

40.  The  magnetic  field  about  a  current 84 

41.  The  solenoid  and  the  electromagnet 84 

42.  Magnetic  induction  and  permeability 85 

43.  The  force  on  a  current  in  a  magnetic  field 86 

H.  INDUCTANCE. 

44.  The  linking  of  circuits  with  lines  of  magnetic  flux 87 

45.  Induced  electromotive  force 88 

46.  Self  inductance 90 

47.  Mutual  inductance 91 

48.  Energy  relations  in  inductive  circuits 92 

I.  ALTERNATING  CURRENT. 

49.  Reactance 93 

50.  Nature  of  an  alternating  current 93 

51.  Average  and  effective  values  of  alternating  current 95 

52.  Circuit  with  resistance  only 97 

53.  Phase  and  phase  angle 97 

54.  Alternating  current  in  a  circuit  containing  inductance 

only 98 


TABLE  OF   CONTEXTS.  9 

Page. 

55.  Circuit  containing  inductance  and  resistance 100 

56.  Charging  of  a  condenser  in  an  alternating  current  circuit.  102 

57.  Circuit  containing  capacitance,  inductance,  and  resist- 

ance   104 

58.  The  alternating  current  transformer 105 

J.  MEASURING  INSTRUMENTS. 

59.  Hot  wire  instruments 106 

60.  Magnetic  instruments 108 

Chapter  2.  Dynamo-Electric  Machinery. 

61.  Generators  and  motors 115 

A.  THE  ALTERNATOR. 

62.  Production  of  emf.  by  revolving  field 115 

63.  Direction  of  emf 117 

64.  Emf.  curve 117 

65.  Cycle,  period,  frequency 117 

66.  Multipolar  magnets 118 

67.  Field  and  armature 118 

68.  Coil-wound  armature 119 

69.  Concentrated  and  distributed  windings 121 

70.  Magnetic  circuit 121 

71.  Field  excitation 124 

72.  Stator  and  rotor 125 

73.  Arrangement  of  parts 125 

74.  Other  forms  of  alternator 125 

75.  Polyphase  alternator 128 

B.  ALTERNATOR  THEORY,  LOSSES,  ETC. 

76.  Equations  for  frequency  and  emf 132 

77.  Dependence  of  driving  power  on  current 131 

78.  Losses 133 

79.  Rating.     Name  plate  data 135 

80.  Efficiency 136 

81.  Regulation „ 136 

82.  Armature  impedance  and  armature  reaction 137 

83.  Effect  of  power  factor  on  regulation 137 

84.  Effect  of  speed  on  regulation 138 

85.  Voltage  control 138 


10  TABLE  OF   CONTENTS. 

C.  DIRECT  CURRENT  GENERATORS. 

Page. 

86.  Commutation 138 

87.  Ring  and  drum  winding 141 

88.  Separate  excitation,  series,  shunt,  compound 144 

89.  Characteristics  of  terminal  voltage 146 

90.  Emf .  equation 148 

91.  Voltage  control 149 

92.  Effect  of  varying  speed 149 

D.  SPECIAL  ALTERNATORS  FOR  RADIO  USES. 

93.  Audio  frequency  and  radio  frequency 149 

94.  Audio  frequency  generators 150 

95.  Radio  frequency  generators 161 

E.  MOTORS. 

96.  Uses  of  d.  c.  and  a.  c.  motors 164 

97.  D.c.  shunt  motor 164 

98.  D.c.  series  motor 172 

99.  Other  d.c.  motors 173 

100.  Combination  a.c.  and  d.c.  motors 173 

101.  Induction  motors 173 

F.  MOTOR-GENERATORS  AND  DYNAMOTORS. 

102.  Motor-generators 175 

103.  Rotary  converters. 177 

104.  Dynamotors 177 

105.  Double  current  generators 178 

106.  Common  troubles 179 

Chapter  3.  Radio  Circuits. 

A.  SIMPLE  RADIO  CIRCUITS. 

107.  The  simplicity  of  radio  theory 182 

108.  The  simple  series  circuit 183 

109.  Series  resonance 185 

110.  Tuning  the  circuit  to  resonance 190 

111.  Resonance  curves 191 

112.  The  wavemeter 193 

113.  Parallel  resonance 195 

114.  Capacitance  of  inductance  coils 199 


TABLE   OF   CONTENTS.  11 

B.  DAMPING. 

Page. 

115.  Free  oscillations 200 

116.  Frequency,  damping,  and  decrement 205 

C.  RESISTANCE. 

117.  Resistance  ratio  of  conductors 208 

118.  Brush,  spark,  dielectric,  and  radiation  resistance 211 

D.  COUPLED  CIRCUITS. 

119.  Kinds  of  coupling 212 

120.  Double  hump  resonance  curve 214 

121.  Forced  oscillations 216 

122.  Free  oscillations  of  coupled  circuits  with  small  damping.  218 

123.  Impulse  excitation.     Quenched  gap 221 

Chapter  4.  Electromagnetic  Waves. 

A.  WAVE  MOTION. 

124.  Three  ways  of  transmitting  energy 223 

125.  Properties  of  wave  motion 223 

126.  Wave  trains,  continuous  and  discontinuous 224 

B.  PROPAGATION  or  WAVES. 

127.  Waves  propagated  by  elastic  properties  of  medium 225 

128.  Properties  of  electromagnetic  waves 225 

129.  Modification  of  waves  in  free  space  near  earth 226 

130.  Static 228 

C.  THEORY  OP  PRODUCTION  AND  RECEPTION  OF  ELECTROMAGNETIC 

WAVES. 

131.  Magnetic  field  produced  by  moving  lines  of  electric  dis- 

placement   229 

132.  Mechanism  of  radiation  from  a  simple  oscillator 230 

133.  Action  in  receiving 232 

D.  TRANSMISSION  FORMULAS. 

134.  Statement  of  formulas 234 

135.  Examples  of  use 235 

136.  General  deductions . .  235 


12  TABLE  OF   CONTENTS. 

E.  DEVICE  FOR  RADIATING  AND  RECEIVING  WAVES. 

Page. 

137.  Description  of  the  antenna 236 

138.  Different  types 238 

139.  Current  and  voltage  distribution  in  an  antenna 239 

140.  Action  of  the  ground.     Counterpoises 240 

F.  ANTENNA  CHARACTERISTICS. 

141.  Capacitance 242 

142.  Inductance 243 

143.  Resistance 243 

144.  Wave  length  and  its  measurement 244 

145.  Harmonics  of  wave  length 246 

146.  Directional  effect 246 

G.  ANTENNA  CONSTRUCTION. 

147.  Towers  and  supports 247 

148.  Insulators 247 

149.  Antenna  switch.     Conductors 248 

150.  Grounds  and  counterpoises 249 

H.  CLOSED  COIL  AERIALS. 


151.  Directional  curve 

152.  Constants  of  closed  coil  aerials. 


Chapter  5.  Apparatus  for  Transmission  and  Reception  (Exclusive 
of  Vacuum  Tubes). 

A.  APPARATUS  FOR  DAMPED  WAVE  TRANSMISSION. 

153.  Function  of  transmitting  apparatus 254 

154.  Simple  spark  discharge  apparatus 254 

155.  Transmitting  condensers 257 

156.  Spark  gaps 257 

157.  Simple  induction  coil  set 262 

158.  Operation  of  induction  coils  from  power  lines 263 

159.  Portable  transmitting  sets 264 

160.  Simple  connections  for  the  production  of  electric  waves.  265 

161.  Inductively  coupled  transmitting  set 268 

162.  Direct  coupled  transmitting  set 270 

163.  Comparison  of  coupled  and  plain  antenna  sets 271 

164.  Tuning  and  resonance 272 


TABLE   OF   CONTENTS.  13 

Page. 

165.  Coupling 272 

1G6.  Damping  and  decrement 274 

167.  Additional  appliances 275 

168.  Adjustment  of  a  typical  set  for  sharp  wave  and  radiation.  277 

169.  Efficiency  of  the  set 278 

170.  Calculations  required  in  design 278 

171.  Simple  field  measurements 283 

B.  APPARATUS  FOR  UNDAMPED  WAVE  TRANSMISSION. 

172.  Advantages  of  undamped  oscillations 287 

173.  Use  of  high  frequency  alternators 287 

174.  Arc  sets 288 

175.  Calibration  and  adjustment  of  sets 290 

C.  APPARATUS  FOR  RECEPTION  OF  WAVES. 

176.  General  principles 290 

177.  Typical  circuits  for  reception  of  damped  waves 293 

178.  Typical  circuits  for  reception  of  undamped  waves 299 

179.  Crystal  detectors 302 

180.  Telephone  receivers 305 

181.  Receiving  coils  and  condensers 306 

182.  Measurement  of  received  current 310 

Chapter  6.  Vacuum  Tubes  in  Radio  Communication. 

183.  Introduction 31 1 

A.  ELECTRON  FLOW  IN  VACUUM  TUBES. 

184.  Current  in  a  two-electrode  tube 311 

185.  Actual  forms  of  two-electrode  tubes 314 

186.  The  three-electrode  tube 315 

187.  Effect  of  grid 317 

188.  Characteristic  curve 317 

189.  Effect  of  an  alternating  emf.  applied  to  grid 319 

190.  Practical  forms  of  three-electrode  tubes 320 

B.  THE  VACUUM  TUBE  AS  A  DETECTOR. 

191.  Simple  detector  circuit  and  explanation  of  its  action 322 

192.  Effect  of  incoming  signals  upon  the  plate  current 325 


14  TABLE   OF   CONTENTS. 

C.  THE  VACUUM  TUBE  AS  AN  AMPLIFIER. 

Page. 

193.  General  principle 326 

194.  Elementary  theory  of  amplification 328 

195.  Audio  frequency  amplification 330 

196.  Regenerative  amplification 330 

197.  Vacuum  tube  amplifier  with  crystal  detector 331 

D.  THE  VACUUM  TUBE  AS  A  GENERATOR. 

198.  Conditions  for  oscillation 332 

199.  Practical  considerations  in  using  vacuum  tubes  as  oscil- 

lation generators 334 

200.  Tubes  suitable  for  developing  considerable  power 335 

201.  Heterodyne  and  autodyne  receiving  by  vacuum  tubes. .  336 

E.  RADIO  TELEPHONY. 

202.  Voice  modulation  of  radio  currents  by  vacuum  tubes. .  337 

203.  Other  methods  of  voice  modulation 339 

204.  Practical  use  of  vacuum  tubes  in  radio  telephony 339 

Appendices. 

APPENDIX  1.  SUGGESTED  LIST  OP  LABORATORY  EXPERIMENTS.  342 

APPENDIX  2.  UNITS 350 

APPENDIX  3.  SYMBOLS  . .  354 


INTRODUCTION. 

1.  What  Radio  Communication  Means. — In  military  service  all 
possible  means  of  communication  are  used,  including  the  most 
primitive.  However,  the  best  and  most  rapid  are  the  electrical 
methods.  These  include  the  ordinary  wire  telegraph  and  telephone 
and  the  wireless  or  radio  apparatus.  Without  wire  connecting  lines, 
radio  messages  are  sent  from  one  point  to  another  on  the  battle  front, 
from  ship  to  shore,  across  the  oceans,  to  airplanes,  and  even  to 
submerged  submarines. 

When  a  pebble  is  thrown  into  the  smooth  water  of  a  pond  it  starts 
a  series  of  circular  ripples  or  waves,  which  spread  out  indefinitely 
with  a  speed  of  a  few  hundred ths  of  a  meter1  per  second.  Similarly, 
an  electric  disturbance  starts  electric  waves,  which  spread  out  in 
all  directions,  and  travel  with  the  velocity  of  light,  or  300,000,000 
meters  per  second.  It  is  by  means  of  these  electric  waves  that  radio 
messages  are  sent. 

In  order  to  make  use  of  electric  waves  for  the  practical  purpose 
of  sending  messages,  it  is  necessary — 

(a)  To  produce  regular  electric  disturbances  in  a  circuit  which 
start  the  waves.  (These  disturbances  are  electric  currents  which 
reverse  rapidly  in  direction.) 

(6)  To  get  the  waves  out  into  surrounding  space,  through  which 
they  travel  with  great  speed.  (This  is  done  by  means  of  the  trans- 
mitting antenna.) 

(c)  By  means  of  these  waves,  to  set  up  electric  currents  in  a 
receiving  circuit  at  the  distant  station.     (The  device  which  these 
waves  strike  as  they  come  in,  and  which  turns  them  over  to  the 
receiving  circuit,  is  called  the  receiving  antenna.) 

(d)  To  change  these  currents  so  that  they  may  be  detected  by 
electric  instruments.     (The  operator  usually  receives  the  message 
through  signals  in  a  telephone  receiver.) 

The  student  of  radio  communication  needs  a  more  thorough 
knowledge  of  electrical  theory  than  that  needed  for  some  branches 

i  The  meter  and  other  units  a-e  explained  in  Appendix  2,  p.  350. 

15 


16  INTRODUCTION. 

of  electrical  work.  This  fact  needs  emphasis  for  the  beginner.  Of 
course  a  man  can  learn  to  operate  and  care  for  apparatus  without 
having  a  real  understanding  of  its  underlying  principles.  It  only 
requires  that  he  have  a  certain  type  of  memory,  industry,  and  a 
little  common  sense.  But  a  man  with  only  this  kind  of  knowledge 
of  his  subject  is  of  limited  usefulness  and  resourcefulness,  and  can 
not  advance  very  far.  The  real  radio  man  must  have  some  training 
in  the  whole  subject  of  electricity  and  magnetism,  as  well  as  a  rather 
intimate  familiarity  with  some  restricted  parts  of  it.  An  under- 
standing of  radio  communication  requires  some  knowledge  of  the 
following  subjects: 

(a)  Direct  and  alternating  currents  and  dynamo  machinery. 

(6)  High  frequency  alternating  currents,  including  the  subject  of 
condenser  discharge. 

(c)  Conduction  of  electric  current  in  a  vacuum  as  well  as  in  wires. 

(d)  Electric    waves,    which    involves    some    acquaintance    with 
modern  ideas  of  electricity  and  the  ether. 

(e)  The  apparatus  used  for  the  production  and  reception  of  elec- 
tric waves. 

2.  Fundamental  Ideas  of  the  Electric  Circuit. — It  is  common 
knowledge  that  a  battery  supplies  what  is  known  as  a  current  of 
electricity.  To  obtain  the  current  there  must  be  a  complete  closed, 
conducting  path  from  the  battery  through  the  apparatus  which  is 
to  be  acted  on  by  the  current,  and  back  again  to  the  battery. 

For  example,  when  connecting  up  an  electric  bell,  a  wire  is 
carried  from  one  binding  post  of  the  battery  (Fig.  1)  to  one  of  the 
binding  posts  of  the  bell,  and  a  second  wire  is  brought  from  the 
other  binding  post  of  the  bell  back  to  the  remaining  binding  post 
of  the  battery.  Any  break  in  the  wire  immediately  causes  the  cur- 
rent to  stop  and  the  bell  to  be  silent.  This  furnishes  an  easy  method 
of  controlling  the  ringing  of  the  bell,  since  it  is  only  necessary  to 
break  the  circuit  at  one  point  to  stop  the  current,  or  to  connect 
across  the  gap  with  a  piece  of  metal  to  start  the  current  going  again. 
Thus  we  have  the  button  for  accomplishing  the  act  of  control,  and 
the  battery  supplies  the  energy  required  to  ring  the  bell. 

Similar  considerations  apply  when  we  are  using  the  city  lighting 
circuit.  Wires  are  brought,  more  or  less  directly,  from  the  lighting 
station  to  the  lamp,  and  a  small  break  in  the  path  through  the  socket 
is  provided.  This  can  be  bridged  by  a  metal  spring  actuated  by 
the  key.  Or  the  opening  and  closing  of  the  circuit  can  be  accom- 


INTRODUCTION. 


17 


plished  by  a  similar  mechanism  in  the  wall  of  the  room,  or  by  a 
knife  switch  (Fig.  2)  in  a  small  cupboard. 

Sometimes  the  lamps  suddenly  go  out,  and  we  say  that  a  fuse  has 
been  blown.  A  short  length  of  wire,  through  which  the  current 
has  been  passing,  is  of  an  easily  fusible  metal  which  has  melted 
away  because  too  strong  a  current  has  been  passing.  Or  it  may  be 
that  it  has  become  necessary  to  open  a  switch  at  the  power  house. 
It  makes  absolutely  no  difference  where  the  break  is  made  in  the 
circuit,  the  result  is  the  same;  the  current  suddenly  stops.  Elec- 
tricity must,  then,  be  regarded  as  flowing  in  every  part  of  the  circuit, 


Ha.  1 


Fio.5 


A  CtaJTery  Circuit  is  liKe  a  (oifoe 
circuit  fv\  I  of  water 


so  that  electricity  is  leaving  the  battery  or  dynamo  at  one  side, 
and  coming  back  to  it  at  the  other  side. 

Current. — The  current  flowing  in  a  circuit  is  no  stronger  at  one 
point  of  the  circuit  than  at  another.  This  can  be  proved  by  con- 
necting a  measuring  instrument  called  an  ammeter  into  the  cir- 
cuit at  different  points,  a,  6,  or  c,  Fig.  2.  It  is  found  to  register 
the  same  at  whatever  point  this  test  is  made.  A  useful  illustration 
of  the  electric  circuit  is  a  closed  circuit  of  pipe  (Fig.  3)  completely 
filled  with  water,  and  provided  with  a  pump,  P,  or  some  other 
device  for  causing  the  water  to  circulate.  The  amount  of  water 
which  leaves  a  given  point  in  each  second  is  just  the  same  as  the 
amount  which  arrives  in  the  same  length  of  time.  Now  in  the 
electric  circuit  we  have  no  material  fluid,  but  we  suppose  that  there 
97340°— 19 2 


18  INTRODUCTION. 

exists  a  substance,  which  we  call  electricity.  Electricity  behaves 
in  the  electric  circuit  much  like  an  incompressible  fluid  in  a  pipe 
line.  We  are  very  sure  that  electricity  is  not  like  any  material 
substance  which  we  know,  but  the  common  practice  among  students 
and  shop  men  of  calling  it  "juice"  shows  that  they  think  of  it  as 
like  a  fluid.  We  will,  then,  imagine  the  electric  current  to  be  a 
stream  of  electricity  flowing  around  the  circuit. 

One  way  of  measuring  the  rapidity  with  which  water  is  flowing 
is  to  let  it  pass  through  a  meter  which  registers  the  total  number 
of  quarts  or  gallons  which  pass  through.  By  dividing  the  quantity 
by  the  time  it  has  taken  to  pass  we  obtain  the  rapidity  of  flow.  There 
are  instruments  by  means  of  which  it  is  possible  to  measure  the  total 
quantity  of  electricity  which  passes  any  point  in  the  circuit  during  a 
certain  time.  If  we  divide  this  quantity  by  the  time,  we  obtain 
the  amount  of  electricity  which  has  passed  in  one  second.  This  is  a 
measure  of  the  current  strength. 

In  practical  work,  however,  the  strength  of  the  current  is  meas- 
ured by  instruments  (ammeters)  which  show  at  each  moment  just 
how  strong  the  current  is,  in  somewhat  the  same  manner  as  we  may 
estimate  the  swiftness  of  a  stream  by  watching  a  chip  on  the  surface. 
This  kind  of  an  instrument  enables  us  to  tell  at  a  glance  what  the 
current  is  without  the  necessity  for  a  long  experiment,  and  further 
we  may  detect  changes  in  the  strength  of  the  current  from  moment  to 
moment.  In  this  connection  it  will  be  remembered  that  two  meas- 
uring instruments  are  to  be  found  on  an  automobile.  The  speed- 
ometer shows  what  the  speed  of  the  car  is  at  each  moment,  so  that 
the  driver  may  know  instantly  whether  he  is  exceeding  the  speed 
limit,  and  govern  himself  as  he  sees  fit.  The  other  instrument  shows 
how  many  miles  have  been  covered  on  the  trip,  and  of  course  the 
average  speed  may  be  calculated  from  its  indications,  if  the  length 
of  the  trip  has  been  timed.  The  instrument  for  measuring  total 
quantity  of  electricity  corresponds  to  the  recorder  of  the  total  miles 
traversed;  the  ammeter  corresponds  to  the  speedometer. 

Electromotive  Force. — The  water  will  not  flow  in  the  pipe  line, 
Fig.  3,  unless  there  is  some  force  pushing  it  along,  as,  for  example, 
a  pump,  and  it  cannot  be  kept  flowing  without  continuing  the  pres- 
sure. Electricity  will  not  flow  in  a  circuit  unless  there  is  a  battery 
or  other  source  of  electricity  in  the  circuit.  The  battery  is  for  the 
purpose  of  providing  an  electric  pressure.  To  this  is  given  the  name 
"electromotive  force  "—that  is,  a  force  which  moves  the  electricity. 


IJsTEODUCTION. 


19 


This  is  usually  abbreviated  to  "emf."  The  larger  the  number  of 
cells  which  are  joined  in  the  circuit  the  greater  the  electric  pressure 
and  the  larger  the  current  produced,  just  as  the  rapidity  of  flow  of 
the  water  in  the  pipe  line  may  be  increased  by  increasing  the  pump 
pressure. 

Resistance. — There  is  always  some  friction  in  pipe,  whatever 
its  size  or  material,  and  this  hinders  the  flow  of  the  water  to  some 
extent.  If  it  were  not  for  the  friction,  the  water  would  increase 
indefinitely  in  speed.  Similarly,  there  is  friction  in  the  electric 
circuit.  This  is  called  the  ''resistance  "  of  the  circuit.  The  greater 
the  resistance  the  smaller  the  current  which  can  be  produced  in 
the  circuit  by  a  given  battery,  just  as  the  greater  the  friction  the  less 


FIQ.4 


FIC3.5 


resistance  by 
(wtidtlly  closed  v<xlve. 


rapid  the  flow  of  water  with  a  given  pump  acting.  A  resistance  coil 
at  any  point  in  the  circuit  corresponds  to  a  partially  closed  valve  in 
the  pipe  at  any  point  (Fig.  4). 

Steady  and  Variable  Currents. — A  pump  producing  a  steady  pres- 
sure gives  rise  to  a  steady  flow  of  water.  The  same  is  true  of  batteries 
and  certain  dynamos  which  produce  a  steady  emf.  A  steady 
electric  current  in  one  direction  is  called  a  " direct  current."  We 
may  suppose,  however,  that  the  water  is  given  a  succession  of  pushes 
all  in  the  same  direction,  but  separated  by  intervals  when  the  water 
is  not  being  pushed.  Such  a  case  occurs  in  the  circulation  of  the 
blood  by  the  heart  beats.  Likewise,  a  current  of  this  nature  may 


20  INTRODUCTION. 

be  produced  in  a  circuit  where  the  emf.  acts  intermittently.  To 
such  a  current  the  name  "pulsating  current"  is  very  appropriately 
applied. 

A  very  important  variety  of  current  for  radio  work  is  that  known 
as  "alternating  current."  This  is  analogous  to  the  kind  of  flow 
which  would  be  produced  if,  instead  of  being  acted  on  by  a  pump, 
the  water  were  agitated  by  a  paddle  which  moved  back  and  forth 
rapidly  over  a  short  distance,  without  traveling  beyond  certain 
limits.  Under  this  impetus  the  water  no  sooner  gets  up  speed  in 
one  direction  than  it  is  compelled  to  slow  up  and  then  gather  speed 
in  the  opposite  direction,  and  so  on  over  and  over  again.  The  water 
simply  surges,  first  in  one  direction,  and  then  in  the  other,  so  that  a 
small  object  suspended  in  the  water  would  not  travel  continuously 
around  the  pipe  line,  but  would  simply  oscillate  back  and  forth  over 
a  short  distance. 

Effect  of  Condenser. — As  a  further  case,  let  us  suppose  that  an 
elastic  partition  E  is  arranged  in  the  pipe  (Fig.  5),  so  that  no  water 
canflow  through  or  around  it.  If  a  pump  P,  or  a  piston,  acts  steadily, 
the  water  moves  a  short  distance  until  the  partition  is  stretched 
enough  to  exert  a  back  pressure  on  the  water  equal  to  the  pressure  of 
the  pump,  and  then  the  movement  of  the  water  as  a  whole  ceases. 
If,  on  the  contrary,  a  reciprocating  motion  is  given  to  the  water  by  P, 
the  water  moves  back  and  forth,  stretching  the  partition  first  in  one 
direction  and  then  in  the  other,  and  the  water  surges  back  and  forth 
between  short  limits  which  are  determined  by  the  elasticity  of  the 
partition.  We  have  in  this  case  an  alternating  current  of  water  in 
spite  of  the  presence  of  the  partition. 

An  electric  condenser  acts  just  like  an  elastic  partition  in  a  circuit. 
No  direct  current  can  flow  through  it,  but  an  alternating  current,  of 
an  amount  depending  on  the  nature  of  the  condenser,  can  flow  when 
an  alternating  emf.  acts  on  the  circuit. 

As  an  extreme  case,  we  may  imagine  the  pipe  line  replaced  by 
a  long  tube  filled  with  water  and  the  ends  closed  by  elastic 
walls  (Fig.  6).  Suppose  an  alternating  pressure  to  be  given 
to  the  water  in  the  tube,  or  even  let  the  tube  be  tipped,  first  in  one 
direction  and  then  in  the  other.  The  water  will  oscillate  back  and 
forth  a  short  distance  in  the  tube,  first  stretching  the  wall  at  one  end 
and  then  the  wall  at  the  other.  A  small  alternating  flow  is  thus  set 
up,  although  there  is  not  a  complete  circuit  for  the  water  to  flow 
through.  Analogous  to  this  case  is  that  of  the  electrical  oscillation 


INTRODUCTION.  21 

of  an  antenna.  Such  a  flow  of  electricity  without  a  complete  circuit 
is  called  a  ' '  displacement  current. "  It  is  always  necessary,  in  order 
to  produce  a  displacement  current,  that  the  circuit  shall  have  elec- 
trical elasticity  somewhere;  that  is,  that  an  electric  condenser 
shall  be  present. 

The  importance  of  the  electric  current  lies  in  the  fact  that  it  is 
an  energy  current.  A  current  of  water  transports  energy;  so  does  a 
current  of  air.  It  is  the  motion  that  counts,  and  to  utilize  the 
energy  of  motion  we  must  do  something  tending  to  stop  the  motion. 
Any  material  substance,  by  virtue  of  its  mass,  can  be  made  to  act 
as  a  vehicle  for  transporting  energy  from  one  place  to  another  pro- 
vided only  it  is  set  into  motion.  In  the  case  of  the  electric  current, 
we  do  not  need  to  inquire  whether  electricity  has  mass.  We  are 
concerned,  in  the  use  of  electrical  apparatus,  with  the  transforma- 
tion of  the  energy  of  the  current  into  other  familiar  forms  of  energy — 
heat,  light  and  motion.  The  electric  current  is  the  vehicle  by 
which  we  transmit  energy  from  the  central  station  to  the  consumer, 
and  we  are  not,  for  practical  purposes,  concerned  with  the  method 
of  carrying  the  energy,  any  more  than  we  need  to  inquire  into  the 
nature  of  the  belt  by  which  mechanical  energy  is  carried  from  one 
wheel  to  another,  or  into  the  chemical  nature  of  the  water  which  is 
furnishing  the  power  in  a  hydraulic  plant. 

The  electric  current  itself  cannot  be  seen,  felt,  smelt,  heard,  or 
tasted.  Its  presence  can  be  detected  only  by  its  effects — that  is, 
by  what  happens  when  it  gives  up  some  of  its  energy.  Thus,  an 
electric  current  may  give  up  some  of  its  energy,  and  cause  a 
motor  to  turn.  Electrical  energy  has  been  given  up,  and  mechan- 
ical energy  takes  its  place.  Similarly,  electric  energy  may  dis- 
appear and  heat  or  light  may  appear  in  its  place,  or  a  chemical 
effect  may  arise.  When  a  person  feels  an  electric  shock,  it  is  not 
the  current  itself  he  feels,  but  the  muscular  contractions  caused 
by  the  passage  of  the  current.  The  electric  lamp  has  an  effect  on 
the  eye.  We  do  not,  however,  see  the  electric  current  in  the  lamp, 
but  the  effect  on  the  eye  is  due  to  the  light  waves  sent  off  by  the 
hot  filament.  The  energy  of  the  current  has  been  changed  over 
into  heat  in  the  lamp.  When  we  hear  a  buzzing  in  the  telephone, 
it  is  not  the  electric  current  we  hear,  but  merely  the  vibration  of 
the  thin  diaphragm.  The  electric  current  has  used  some  of  its 
energy  in  moving  the  diaphragm.  The  acid  taste  noticed  when 
the  tongue  is  bridged  across  the  poles  of  a  dry  battery  is  due  to  the 


22  INTRODUCTION. 

chemical  decomposition  of  the  saliva  into  other  compounds  as  a 
result  of  the  passage  of  the  current  through  it. 

In  the  next  section,  the  electric  current  is  studied  through  the 
effects  it  produces,  and  in  later  sections  it  is  given  a  more  exact 
and  detailed  treatment. 


CHAPTER  1. 

ELEMENTARY  ELECTRICITY. 
A.  Electric  Current. 

3.  Effects  of  Electric  Current. — Electricity  may  be  stored  in  an 
apparatus  called  a  condenser  (see  Sec.  30)  as  air  is  stored  under 
pressure  in  a  tank,  and  certain  characteristic  effects  accompany 
this  condition.  However,  the  most  practical  applications  of  elec- 
tricity follow  from  the  movement  of  electric  charges — that  is,  elec- 
tric current.  Quantity  of  electricity  is  of  importance  in  connection 
with  such  subjects  as  electrons  (Sec.  6)  and  capacitance. 

A  wire  in  which  an  electric  current  is  flowing  usually  looks 
exactly  like  a  wire  without  current.  Our  senses  are  not  directly 
impressed  by  the  phenomena  of  electricity,  and  hence  it  is  neces- 
sary to  depend  upon  certain  effects  which  are  associated  with  the 
flow  of  current  through  a  conductor  when  it  is  desired  to  determine 
whether  or  not  a  current  exists.  Some  of  these  effects  are  as  follows: 

(a)  If  a  straight  wire  is  brought  near  a  small  magnet,  such  as  a 
compass  needle,  which  is  so  placed  that  the  axis  about  which  it 
turns  is  parallel  to  the  axis  of  the  wire  (Fig.  7)  then  the  needle  is 
deflected  a  certain  amount  and  tends  to  become  tangent  to  a  circle 
about  the  wire.  It  then  remains  in  the  new  position  as  long  as  the 
current  does  not  vary. 

(6)  A  wire  with  a  current  passing  through  it  will  be  at  a  higher 
temperature  than  the  same  wire  before  the  current  flows.  This 
can  be  readily  detected  by  a  sensitive  thermometer,  and  under 
some  conditions,  as  in  an  ordinary  incandescent  lamp,  the  rise  of 
temperature  is'  so  great  as  to  cause  the  filament  to  glow. 

(c)  If  the  wire  through  which  the  current  is  flowing  is  cut,  and 
if  the  separated  ends  are  attached  respectively  to  two  metallic 
plates  immersed  in  a  solution  of  some  substance  like  copper  sulphate, 
there  will  be  a  chemical  change  in  the  solution  accompanied  by  a 
deposition  of  the  metal  copper  on  one  of  the  plates. 

The  attention  of  the  student  should  be  fixed  upon  these  effects 
of  the  current,  rather  than  upon  the  current  itself.  It  is  in  terms 


24 


RADIO    COMMUNICATION. 


of  these  effects  that  electric  currents  are  detected,  measured  and 
applied.  Thus  the  magnetic  effect  is  the  basis  of  dynamo-electric 
machinery  and  radio  communication;  the  heating  effect  makes 
possible  electric  cooking  and  electric  lighting;  and  the  chemical 
effect  is  the  basis  of  electroplating.  All  three  effects  are  utilized 
in  making  electric  measurements. 

It  must  be  kept  in  mind  that  such  expressions  as  "flow"  and 
"current,"  and  many  other  electrical  terms  are  merely  survivors 
from  an  earlier  day  when  electricity  was  supposed  to  be  a  fluid, 
which  actually  flowed.  Such  terms  are,  however,  helpful  in 
forming  mental  pictures  of  the  real  phenomena  of  electricity. 


Md&nefj'c  filld  about  A 
straight  wire.l 
Current  flo  Iwin^  down. 


FIQ 


.  hand 

Wood  Screw 


.._w  „._  l|ield  db^uta  strdi^hf  wire 
Current  |f iijwin^,  ujj. 


Memory  rule  -\ar  direction  0f  current  <*n4 
lines   of  fore's 


Attention  must  always  be  centered  on  the  facts  and  effects  which 
these  terms  represent  and  the  words  or  phrases  themselves  must 
not  be  taken  too  literally.1 

4.  Magnitude  and  direction  of  current. — By  means  of  the  mag- 
netic effect  it  is  readily  shown  that  electric  current  has  direction. 
If  the  wire  in  Fig.  7  be  withdrawn  from  the  plate,  0,  and  reinserted 
in  the  opposite  direction,  the  compass  needle  will  indicate  a  direc- 
tion (Fig.  8)  nearly  opposite  to  that  of  its  original  position.  The 
same  result  is  secured  by  interchanging  the  wires  at  the  poles  of 
the  battery. 


Read  Franklin  and  MacNutt,  General  Physics,  p.  238. 


RADIO  COMMUNICATION.  25 

The  direction  of  flow  of  electric  current  is  in  any  event  a  matter 
of  arbitrary  definition,  and  in  practice  the  student  will  usually 
determine  the  direction  by  means  of  an  instrument  with  its  terminal 
marked  +  and  — .  It  is  assumed  that  current  enters  the  instrument 
at  the  -f-  terminal  and  leaves  it  at  the  —  terminal. 

The  magnetic  effect  may  also  be  used  in  specifying  the  direction 
of  the  current.  See  Sec.  40.  Again  referring  to  Fig.  7,  it  is  seen 
that  as  the  current  flows  down  through  the  plane,  the  compass 
needle,  at  every  point  in  the  plane,  tends  to  set  itself  tangent  to 
one  of  the  concentric  circles  about  the  wire.  The  north  seeking,  or 
north  pointing  pole  of  the  needle  will  point  in  a  clockwise  direction 
around  the  current  as  the  observer  looks  along  the  conductor  in  the 
direction  of  the  current.  Other  useful  rules  for  remembering  the 
same  relative  directions  are  as  follows: 

(a)  Grasp  the  wire  with  the  right  hand,  and  with  the  thumb 
extended  along  the  wire  in  the  direction  of  the  current.  The  curved 
finger  tips  will  then  indicate  the  direction  of  the  magnetic  effect, 
Fig.  10. 

(6)  Imagine  a  wood  screw  being  advanced  into  a  block  in  the  direc- 
tion of  the  current,  Fig.  9.  The  direction  of  its  rotation  then 
indicates  the  direction  of  the  magnetic  field  around  the  wire  or 
conductor. 

The  student  should  assure  himself  of  complete  familiarity  with 
one  of  these  rules  by  considerable  practice  with  a  small  compass 
and  a  simple  electric  circuit. 

5.  Measurement  of  Electric  Current  and  Quantity  of  Electricity.— 
All  three  of  the  simple  ways  by  which  electric  current  may  be 
detected  (see  Sec.  3)  provide  means  of  current  measurement.  The 
magnetic  effect  of  the  current  may  be  used  by  mounting  a  wire  and 
a  magnet  in  such  positions  that  when  a  current  flows  in  the  wire 
either  the  magnet  or  the  wire  moves.  The  heating  effect  of  the 
current  is  utilized  in  hot  wire  instruments  (Sec.  49),  where  the 
increase  in  length  of  the  heated  wire  is  utilized  to  move  a  pointer 
over  a  dial.  These  principles  are  used  in  a  great  variety  of  instru- 
ments for  the  measurement  of  current.  The  amount  of  current  is 
read  from  the  scale  or  dial  of  the  instrument.  The  scale  is  usually 
graduated  at  the  time  when  the  instrument  is  standardized,  in  a 
unit l  called  the '  'ampere. ' '  The  instruments  are  called  '  'ammeters. " 

i  See  Appendix  2  on  "Units,"  p.  356. 


26  RADIO    COMMUNICATION. 

The  ampere  is  a  unit  the  magnitude  of  which  has  been  denned 
by  international  agreement.  In  its  definition  the  third  effect  of 
the  electric  current,  described  above,  is  made  use  of.  The  mass  of 
a  metal  which  is  deposited  out  of  a  solution  by  an  electric  current 
depends  on  the  product  of  the  strength  of  the  current  by  the  time 
it  is  allowed  to  flow.  Thus  a  certain  current  flowing  for  100  seconds 
is  found,  experimentally,  to  be  able  to  deposit  as  much  of  a  metal  as 
a  current  100  times  as  great  passing  for  one  second,  etc.  Remem- 
bering that  the  strength  of  the  current  is  the  rapidity  of  flow  of 
electricity,  it  is  evident  that  the  product  of  strength  of  current  by 
time  of  flow  gives  the  total  quantity  of  electricity  which  has  passed. 

The  mass  of  a  metal  deposited  by  the  current  is,  then,  propor- 
tional to  the  total  quantity  of  electricity  which  has  flowed  through 
the  solution.  Equal  quantities  of  electricity  will  deposit  different 
masses  of  different  metals,  but  the  mass  of  any  chosen  metal  is  always 
the  same  for  the  same  quantity  of  electricity. 

The  ampere  (properly  called  the  international  ampere)  is  that  un- 
varying current  which,  when  passed  through  a  neutral  solution  of  silver 
nitrate,  will  deposit  silver  at  the  rate  of  .001118  gram  per  second. 

A  convenient  way  of  remembering  this  figure  is  that  it  is  made 
up  of  one  point,  two  naughts,  three  ones,  and  four  twos — 8.  While 
current  could  be  regularly  measured  by  the  process  used  in  estab- 
lishing this  unit  this  is  not  done  in  actual  practice.  The  measuring 
instruments  used  in  actual  measurements  are,  however,  standardized 
more  or  less  directly  in  terms  of  the  unit  thus  defined. 

6.  Electrons. — When  electric  current  flows  in  a  conductor  there 
is  a  flow  of  extremely  small  particles  of  electricity,  called  electrons. 
The  study  of  these  particles  is  important  not  only  in  connection 
with  current  flow,  but  also  in  light  and  heat  and  chemistry.  The 
reason  for  this  is  that  all  matter  contains  them.  Matter  of  all  kinds 
is  made  up  of  atoms,  which  are  extremely  small  portions  of  matter 
(a  drop  of  water  contains  billions  of  them).  The  atoms  contain 
electrons  which  consist  of  negative  electricity.  The  electrons  are 
all  alike,  and  are  in  turn  much  smaller  than  the  atoms.  Besides 
containing  electrons,  each  atom  also  contains  a  certain  amount  of 
positive  electricity.  Normally  the  positive  and  negative  electricity 
are  just  equal.  However,  some  of  the  electrons  are  not  held  so 
firmly  to  the  atom  but  what  they  can  escape  when  the  atom  N  is 
violently  jarred.  When  an  electron  leaves  an  atom,  there  is  then 
less  negative  electricity  than  positive  in  the  atom;  in  this  condition 


RADIO  COMMUNICATION.  27 

the  atom  is  said  to  be  positively  charged.  When  on  the  other  hand 
an  atom  takes  on  one  or  more  extra  electrons,  it  is  said  to  be  nega- 
tively charged. 

The  atoms  in  matter  are  constantly  in  motion,  and  when  they 
strike  against  one  another  an  electron  is  sometimes  removed  from 
an  atom.  This  electron  then  moves  about  freely  between  the  atoms. 
Heat  has  an  effect  upon  this  process.  The  higher  the  temperature, 
the  faster  the  atoms  move  and  the  more  electrons  given  off.  If  a 
hot  body  is  placed  in  a  vacuum,  the  electrons  thus  given  off  travel 
from  the  hot  body  out  into  the  surrounding  space.  This  sort  of  a 
motion  of  electrons  is  made  use  of  in  the  vacuum  tube,  which  is 
the  subject  of  Chapter  8  of  this  book.  The  motion  of  the  electrons 
inside  a  wire  or  other  conductor  is  the  basis  of  electric  current  flow. 
This  is  briefly  discussed,  with  the  various  important  properties  of 
electrons,  in  Circular  No.  74  of  the  Bureau  of  Standards,  page  8. 
(This  circular  will  hereafter  be  referred  to  as  C.  74.) 

B.  Resistance  and  Resistivity. 

7.  Resistance  and  Conductance. — The  flow  of  current  through  a 
circuit  is  opposed  by  a  property  of  the  circuit  called  its  ' '  resistance ' ' 
(symbol  R).  The  resistance  is  determined  by  the  kinds  of  materials 
of  which  the  circuit  is  made  up,  and  also  by  the  form  (length  and 
cross  section)  of  the  various  portions  of  the  circuit.  Provided  that 
the  temperature  is  constant,  the  resistance  is  constant,  not  varying 
with  the  current  flowing  through  the  circuit.  This  important 
relation  is  called  Ohm's  law  and  will  be  discussed  further  in  Section 
14.  All  substances  may  be  grouped  according  to  their  ability  to 
conduct  electricity,  and  those  through  which  current  passes  readily 
are  called  "conducting  materials"  or  "conductors."  while  those 
through  which  current  passes  with  difficulty  are  called  "insulating 
materials"  or  "non-conductors."  However,  there  is  no  known  sub- 
stance which  admits  current  without  any  opposition  whatever^ 
nor  is  there  any  known  substance  through  which  some  small  current 
cannot  be  made  to  pass.  There  is  no  sharp  distinction  between  the 
groups,  as  they  merge  gradually  one  into  the  other.  Nevertheless,  it 
should  be  kept  in  mind  that  conductors  have  a  conducting  power 
which  is  enormously  greater  than  the  conducting  power  of  an  in- 
sulator. The  minute  current  which  can  be  forced  through  an  in- 
sulator under  certain  circumstances  is  aptly  called  a  "leakage  cur- 
rent." An  ideal  insulator  would  be  one  which  would  allow  abso- 


28  RADIO    COMMUNICATION. 

lately  no  current  to  flow.  Examples  of  good  conducting  materials 
are  the  metals  and  that  class  of  liquid  conductors  called  electrolytes. 
Examples  of  insulating  materials  are  dry  gases,  glass,  porcelain, 
hard  rubber,  and  various  waxes,  resins,  and  oils. 

A  circuit  which  offers  but  little  resistance  to  a  current  is  said  to 
have  good  conductance.     Representing  this  by  g  we  may  write 


For  example,  a  circuit  having  a  resistance  of  10  ohms  will  have  a 
conductance  of  0.1  and  one  of  0.01  ohm  will  have  a  conductance  of 
100.  The  unit  of  resistance  called  the  "ohm  "  is  defined  in  terms  of 
a  standard  consisting  of  pure  mercury,  of  accurately  specified  length, 
mass  and  temperature. 

The  international  ohm  is  the  resistance  offered  to  the  flow  of  an  unvary- 
ing current  by  a  column  of  mercury  106.3  centimeters  high  and  weighing 
14.4521  grams  at  a  temperature  ofO°  C. 

For  very  small  resistances,  the  millionth  part  of  an  ohm  is  used  as 
a  unit  and  is  called  the  "microhm."  For  high  resistances  a  million 
ohms  is  used  as  a  unit  and  is  called  the  "megohm." 

The  opposition  to  flow  of  current  referred  to  above  is  analogous 
to  friction  between  moving  water  and  the  inner  surface  of  the  pipe 
through  which  it  flows.  It  is  always  accompanied  by  the  pro- 
duction of  heat.  If  an  unvarying  current  is  maintained  through  a 
conductor,  this  production  of  heat  is  at  a  constant  rate.  The  total 
heat,  produced  in  t  seconds,  is  found  to  be  proportional  to  the 
resistance  of  the  circuit,  to  the  square  of  the  current  and  to  the  time, 
thus 

W=RIH  (2) 

From  this  it  follows  that  R,  for  a  given  portion  of  the  circuit,  might 
be  measured  by  the  heat  generated  in  that  portion.  The  heat  will 
be  measured  in  "joules7'  when  the  current  is  in  amperes,  the  resist- 
ance in  ohms  and  the  time  in  seconds.  To  find  the  heat  in  calories, 
the  relation  W/  J=H  will  be  used,  where  Wis  in  joules  and  /,  (4.18), 
is  the  number  of  joules  in  one  calorie.  The  relation  given  in  equa- 
tion (2)  is  sometimes  called  Joule's  law. 

8.  Resistivity  and  Conductivity.  —  For  a  given  piece  of  wire  of 
uniform  cross  section,  its  resistance  is  found  to  be  proportional 
directly  to  its  length,  and  inversely  to  its  cross  sectional  area;  and 
in  addition  the  resistance  depends  upon  the  kind  of  material  of 


RADIO   COMMUNICATION.  29 

which  the  wire  is  composed.  These  relations  may  be  expressed  in 
the  following  equation 

R=4  (3) 

where  R  is  the  measured  resistance  of  the  sample,  I  is  the  length,  s 
is  its  cross  section  and  p  is  a  constant,  characteristic  of  the  given 
material.  Solving  this  equation  for  p  we  have 

P=RSl  (4) 

If  a  piece  of  material  is  chosen  having  unit  cross  section  and  unit 
length,  it  is  seen  that  p  is  equal  to  the  resistance  of  the  piece,  meas- 
ured between  opposite  faces.  The  factor  p  is  called  the  "resistivity  " 
of  the  substance,  and  is  denned  as  the  resistance  between  opposite 
faces  of  the  unit  cube.  The  ohm  or  the  microhm  is  commonly  used 
as  the  unit  of  resistance  and  the  centimeter  as  the  unit  of  length. 
Instead  of  expressing  resistivity  in  these  units  it  may  also  be  given 
in  terms  of  ohms  per  foot  of  wire  one  mil  (0.001  inch)  in  diameter,  or 
in  ohms  per  meter  of  wire  one  millimeter  in  diameter. 

Another  group  of  resistivity  units  is  based  upon  the  mass  of  a 
sample  instead  of  its  volume,  for  example:  (a)  the  resistance  of  a 
uniform  piece  of  wire  of  one  meter  length  and  of  one  gram  mass; 
or  (6)  the  resistance  of  a  wire  of  one  mile  length  and  of  one  pound 
mass.  Practically,  for  some  purposes,  the  mass  resistivity  is 
preferable  to  the  volume  resistivity  for  the  following  reasons:  (a) 
sufficiently  accurate  measurements  of  cross  section  of  specimens  are 
frequently  difficult,  or,  for  some  shapes,  impossible;  (6)  material 
for  conductors  is  usually  sold  by  weight  rather  than  volume,  and 
hence  the  data  of  greatest  value  are  most  directly  given.  The  mass 
units  and  volume  units  are  readily  interconverted,  provided  that 
the  density  of  the  material  is  known.  If  in  equation  (3)  we  substi- 
tute for  s  the  value  of  v/l,  where  v  is  the  volume,  and  for  v  its  equiva- 
lent ^ ,  where  ra  is  the  mass  and  d  is  the  density,  we  have 
a 

S-pdJi  (5) 

The  quantity  pdis  called  the  mass  resistivity  of  the  material.  The 
volume  resistivity  may  then  be  transformed  into  mass  resistivity, 
or  vice  versa,  taking  care  that  all  the  quantities  are  given  in 


30  RADIO    COMMUNICATION. 

consistent  units.  As  examples  of  resistance  the  following  wil 
be  useful: 

1.  One  ohm  is  the  resistance  of  about  157  feet  of  number  18  copper 
wire,  (diameter  about  1  mm.,  or  40  mils  or  0.04  in.). 

2.  One  thousand  feet  of  number  10  iron  wire  (diameter  about  2.5 
mm.,  or  102  mils  or  0.1  in.)  has  a  resistance  of  about  6.5  ohms. 

Tables  of  resistivity  for  various  materials  are  given  in  Table  21, 
C.  74. 

Just  as  conductance  is  the  reciprocal  of  resistance  when  con- 
sidering the  properties  of  a  circuit  as  a  whole,  so  "conductivity"  is 
the  reciprocal  of  resistivity  when  considering  the  properties  of  a 
given  material.  Its  unit  is  the  "mho,"  or  "reciprocal  ohm." 

9.  Temperature  Coefficient.  —  The  electrical  resistance  of  all  sub- 
stances is  found  to  change  more  or  less  with  any  change  in  tem- 
perature. All  pure  metals  and  most  of  the  metallic  alloys  show  an 
increased  resistance  with  rising  temperature.  Carbon  and  most 
liquid  conductors  like  battery  solutions,  show  a  decrease  in  resistance 
as  the  temperature  increases.  Experiment  shows  that  the  resistance 
at  a  temperature  t  can  be  calculated,  if  the  resistance  at  zero  tem- 
perature (melting  point  of  ice)  has  been  measured.  The  formula  is 

R^R.+R^t  (G) 

where  R0  is  the  resistance  of  the  sample  at  zero,  and  «0  is  the  change 
in  1  ohm  when  the  temperature  changes  +>rom  zero  to  1°  C.  The 
factor  a0  is  called  the  "temperature  coefficient"  of  resistance  for  the 
material.  Solving  equation  (6)  for  «0  we  have 


Equation  (7)  shows  that  a0  is  the  value  of  the  change  in  the  resistance 
per  ohm  per  degree  change  in  temperature,  or  it  is  the  fractional 
change  of  the  total  resistance  for  1  degree  change  in  temperature.  If 
the  resistance  of  the  material  decreases  with  a  rise  in  temperature, 
then  the  temperature  coefficient  is  said  to  be  negative. 

If  a  reference  temperature  £t  is  chosen,  which  is  not  zero,  then  the 
resistance  R2,  at  some  other  temperature  £2>  which  is  higher  than 
<u  may  be  found  from  the  resistance  Rl  at  it  by  the  following 
equation, 

/22=-Ri[l+«i(«2-*i)]  (8) 

Calculations  of  this  sort  are  simplified  by  the  use  of  a  table  of  values 
of  a,  for  various  initial  reference  temperatures.  See  Table  21,  C.  74. 


RADIO   COMMUNICATION. 


31 


10.  Current  Control. — In  electrical  work  the  need  is  constantly 
arising  for  adjusting  a  current  to  a  specified  value.  This  is  usually 
done  by  varying  the  resistance  of  the  circuit.  Changes  in  the  re- 
sistance of  a  circuit  can  be  made  by  means  of  resistors,  which  consist 
in  general  of  single  resistance  units,  or  groups  of  such  units  made  of 
suitable  material.  These  may  be  variable  or  fixed  in  value.  Vari- 
able resistors  are  frequently  called  "resistance  boxes"  or  "rheos- 
tats," depending  on  their  current  carrying  capacity  and  range. 

A  resistance  box  consists  of  a  group  of  coils  of  wire  assembled  com- 
pactly in  a  frame  or  box.  (Figs.  11,  12,  and  13.)  It  is  so  arranged 
that  single  coils  or  any  desired  combination  of  such  coils  may  be 


:ia.u 

Plu£  resistance  bax 


introduced  into  the  circuit  by  manipulating  the  switches  or  plugs. 
The  extreme  range  of  such  a  device  may  be  from  a  hundredth  or  a, 
tenth  of  an  ohm,  up  to  100,000  ohms.  Each  of  its  component  units 
is  accurately  standardized  and  marked  with  its  resistance  value.  By 
this  means,  it  is  possible  to  know  precisely  what  resistance  is  intro- 
duced into  the  circuit  by  the  resistance  box.  The  coils  are  wound 
with  relatively  fine  wire,  and  in  such  a  way  that  they  do  not  have 
any  appreciable  magnetic  fields  about  them.  They  are  intended 
solely  for  carrying  feeble  currents,  usually  no  more  than  a  fraction 
of  an  ampere. 


32 


RADIO    COMMUNICATION. 


The  name  "rheostat"  is,  in  general,  applied  to  a  similar  device, 
but  with  a  larger  current  carrying  capacity  and  a  smaller  range.  Its 
coils  are  usually  open  to  the  air  and  it  may  be  adjusted  continuously 
or  by  steps.  (Figs.  14  and  15.)  The  familiar  groups  of  grids  sup- 
ported beneath  the  floor  of  street  cars  is  a  good  example  of  rheostat. 
The  individual  units  are  not  accurately  measured  and  marked  as 
they  are  in  the  resistance  box,  and  it  is  usually  not  necessary  to  know 
the  values  of  the  separate  steps.  A  frequently  used  resistor  for  large 
currents  is  made  by  immersing  plates  in  a  tank  of  a  conducting 
liquid.  Adjustments  are  made  by  varying  the  distance  between 
the  plates.  For  smaller  ranges,  the  carbon  compression  rheostat  is 
much  used  in  laboratory  work.  In  this  type,  a  number  of  carbon 
Dlates  are  brought  into  more  or  less  intimate  contact  by  a  variable 
screw  pressure. 

Resistors  of  single  fixed  values  are  convenient  for  many  purposes. 
If  they  are  carefully  made  and  precisely  measured  they  'are  often 


called  standard  resistance  coils.  Such  standards  may  be  secured 
in  range  from  0.00001  ohm  to  100,000  ohms,  and  of  any  desired  cur- 
rent carrying  capacity  and  degree  of  precision. 

Banks  of  incandescent  lamps  in  various  arrangements  are  often 
used  as  resistors.  The  resistance  of  such  lamps  is  subject  to  large 
variations  in  value  with  changes  in  temperature.  However,  when 
operating  under  steady  conditions,  either  hot  or  cold,  they  are 
satisfactory  for  many  purposes.  Such  a  rheostat  offers  the  advantage 
of  being  readily  adjustable  by  turning  lamps  off  or  on.  It  is  com- 
pact and  there  is  no  danger  of  overheating. 

11.  Conducting  Materials. — Conducting  materials,  usually  metals 
or  metallic  alloys,  are  utilized  in  electric  circuits  with  two  different 
purposes  in  view.  In  one  case  a  high  degree  of  conductivity  is 


RADIO  COMMUNICATION.  33 

required,  while  in  the  other  case  relatively  high  resistivity  is  de- 
sired. These  cases  will  be  discussed  in  turn. 

(a)  If  the  conductor  is  transmitting  energy  to  a  distant  point  by 
means  of  the  electric  current  it  is  seen  from  equation  (2)  that  some 
energy  will  be  wasted  in  the  conductor  in  the  form  of  heat.  This 
loss  should  be  kept  as  small  as  possible,  and  to  this  end  great  care 
is  taken  in  choosing  the  size  and  material  of  the  conductor.  For 
reasons  of  economy  the  cross  section  must  not  be  too  great,  hence  a 
desirable  material  for  conducting  lines  must  have  low  resistivity 
and  must  be  abundant  and  relatively  cheap  to  produce.  Such  a 
material  is  copper.  Where  lightness  is  important  and  where  in- 
creased dimensions  are  not  a  disadvantage,  aluminum  is  much  used. 
Steel  is  used  where  great  strength  is  desired  and  where  the  current 
is  small,  as  in  telegraph  lines.  For  lines  which  must  stand  great 
strain  and  at  the  same  time  be  good  conductors,  such  as  radio 
antennae,  a  stranded  phosphor  bronze  wire  is  often  used. 

(6)  On  the  other  hand,  a  material  which  is  to  be  used  for  resistor 
coils  should  have  the  following  properties: 

1.  The  resistivity  should  be  high,  so  that  a  large  resistance  may 
be  realized  without  too  great  a  bulk. 

2.  The  resistivity  should  be  constant,  so  that  when  a  coil  is  once 
adjusted  to  a  given  value  there  will  be  no  progressive  changes  in 
its  resistance  as  time  goes  on. 

3.  The  temperature  coefficient  should  be  small,  so  that  changes 
in  temperature  will  not  appreciably  affect  the  resistance  values. 

4.  The  thermoelectric  effect  (see  Sec.  15)  between  the  chosen 
substance  and  copper  or  brass  should  be  small,  so  that  variations  in 
temperature  between  different  parts  of  the  circuit  will  not  cause 
troublesome  thermal  currents. 

Copper,  although  widely  used  as  a  conductor,  has  too  low  a  resis- 
tivity and  too  large  a  temperature  coefficient  to  be  useful  in  resistor 
units.  Iron  likewise  is  neither  high  enough  in  resistivity  nor  con- 
stant enough  in  its  behavior,  except  for  use  in  certain  types  of 
rheostats.  Many  of  the  alloys  of  copper  and  nickel  have  a  suffi- 
ciently high  resistivity,  but  they  develop  large  thermal  emfs.  against 
brass  and  copper,  which  makes  them  undesirable  for  precision 
resistors.  In  the  alloy  manganin,  however,  a  very  satisfactory 
resistance  material  is  realized.  It  has  high  resistivity,  and  practi- 
cally negligible  temperature  coefficient  and  thermoelectric  effect. 
97340°— 19 3 


34  RADIO    COMMUNICATION. 

Table  21,  C.  74,  gives  the  properties  of  some  pure  metals  and 
the  composition  and  electrical  properties  of  certain  of  the  more 
common  alloys. 

Wire  Gauges. — Sizes  of  wires  are  specified  in  two  general  ways, 
either  by  giving  the  actual  diameter  in  millimeters  or  in  mils  (1  mil= 
0.001  in.),  or  by  assigning  to  the  wire  its  place  in  an  arbitrary  series 
of  numbers  called  a  wire  gauge.  Only  two  of  these  arbitrary  wire 
gauges  are  of  importance  in  American  practice,  the  American  Wire 
Gauge  and  the  Steel  Wire  Gauge.  To  avoid  confusion  the  name  of 
the  gauge  must  always  be  given  with  the  gauge  number.  Most  steel 
wire  is  specified  in  terms  of  the  steel  wire  gauge.  Wire  used  in 
electrical  work,  such  as  copper,  aluminum  and  the  copper- nickel 
alloys,  is  specified  in  terms  of  the  American  Wire  Gauge.  This 
is  the  only  gauge  in  which  the  successive  sizes  have  a  definite 
mathematical  relation. 

It  is  convenient  to  remember  that  any  change  of  three  sizes  of 
this  gauge,  doubles  (or  halves)  the  resistance  of  a  wire;  a  change  of 
six  sizes  doubles  (or  halves)  the  diameter,  and  therefore  quadruples 
(or  divides  by  four)  the  resistance  of  the  wires. 

12.  Non-conducting  or  Insulating  Materials. — The  importance  of 
good  conductors,  in  practical  applications  of  electricity,  has  been 
dwelt  on  in  the  preceding  section.  It  is  however  equally  impor- 
tant to  have  non-conducting  materials  in  order  that  electric  current 
may  be  confined  to  definite  and  limited  paths.  Such  materials  are 
commonly  called  insulators  or  dielectrics.  It  is  a  familiar  fact  that 
electric  wires  are  covered  with  layers  of  cotton,  silk,  rubber  and  other 
non-conducting  compounds,  and  are  supported  on  porcelain  knobs 
or  in  clay  tubes.  This  is  done  to  prevent  the  current  from  escaping 
along  a  chance  side  path  before  the  desired  terminal  point  is  reached. 

Strictly,  there  is  no  such  thing  as  a  perfect  non-conductor.  The 
materials  commonly  used  for  this  purpose  have  volume  resistivities 
ranging  from  10,000  ohms  to  1017  ohms  between  opposite  faces  of  the 
unit  cube.  This  means  that  1  volt  impressed  across  such  a  unit 
cube  by  means  of  proper  metal  terminals,  would  cause  a  current  of 

fr°m— "006  to  -L_  ampere  to  flow.     (See  Sec.  13.) 

Most  insulating  substances  show  a  decrease  in  volume  resistivity 
with  increase  in  temperature.  These  changes  are  irregular  and 
sometimes  rapid.  They  are  not  directly  proportional  to  the  changes 
in  temperature.  Humidity  is  of  great  influence,  and  tends  to  lower 


RADIO   COMMUNICATION.  35 

the  volume  resistivity  in  such  materials  as  slate,  marble,  bakelite 
and  hard  fiber.  Very  frequently  surface  leakage  is  of  greater  im- 
portance than  volume  conduction,  and  this  surface  leakage  is  largely 
dependent  upon  the  moisture  film  upon  the  surface.  Some  sub- 
stances acquire  a  surface  film  of  moisture  more  readily  than  others. 
In  any  event,  care  must  be  taken  to  ensure  that  its  effects  are  either 
eliminated  or  allowed  for. 

In  work  involving  high  potential  differences  the  property  of  di- 
electric strength  is  of  greater  importance  than  volume  resistivity. 
If  the  potential  difference  applied  between  opposite  sides  of  a  sheet 
of  dielectric  material  exceeds  a  certain  critical  value,  the  dielectric 
will  break  down,  as  though  under  a  mechanical  stress,  and  a  spark 
will  pass  between  the  terminals.  In  case  the  dielectric  is  a  liquid 
or  a  gas,  its  continuity  is  immediately  restored  after  the  spai*k  has 
passed.  However,  in  a  solid  dielectric  the  path  of  the  spark  dis- 
charge is  a  permanent  defect,  and  if  enough  energy  is  being  supplied 
from  the  source,  a  continuous  current  will  persist,  which  flows 
along  the  arc  or  bridge  of  vapor  formed  by  the  first  spark.  "Di- 
electric strength"  is  a  property  of  the  material  which  resists  this 
tendency  to  break  down.  It  is  measured  in  terms  of  volts  or  kilo- 
volts  required  to  pierce  a  given  thickness  of  the  material.  Values 
of  dielectric  strength  of  air  are  given  in  Chapter  5,  Section  171.  It 
is  a  quantity  that  cannot  be  specified  or  measured  very  precisely, 
because  the  results  vary  with  (a)  the  character  of  the  voltage, 
whether  direct  or  alternating,  (6)  the  distance  between  the  termi- 
nals, (c)  the  time  for  which  the  voltage  is  applied,  and  (rf)  the  shapfe 
of  the  terminals.  The  presence  of  moisture  lowers  the  dielectric 
strength.  Dry  air  is  one  of  the  best  of  the  insulating  substances, 
but  its  dielectric  strength  is  lower  than  that  of  many  liquids  and 
solids. 

In  addition  to  the  constant  currents  which  flow  through  or  over 
insulating  substances,  due  to  the  "body  leakage"  and  "surface 
leakage  "  we  find  two  other  currents  which  are  temporary,  but  which 
it  is  important  not  to  overlook. 

1.  The    "displacement   current"    which   is    discussed    later    in 
Section  29.     This  current  appears  and  becomes  negligible  in  a  very 
short  time,  not  more  than  a  few  thousandths  of  a  second. 

2.  The  "absorption  current"  which  persists  longer  and  is  ob- 
served when  an  emf.  is  applied  to  a  plate  of  a  dielectric  by  means 
of  electrodes  as  in  the  case  of  a  condenser.     (See  Sec.  31.) 


36 


RADIO    COMMUNICATION. 


At  first  there  is  a  considerable  rush  of  current  but  this  falls  off 
with  the  time  at  first  rapidly,  then  more  slowly.  It  may  not  be- 
come negligible  for  several  hours.  It  is  due  to  some  rearrangement 
of  the  molecules  of  the  substance  under  the  stress  of  the  applied 
emf. 

C.  Potential  Difference,  Emf.,  and  Ohm's  Law. 

13.  The  Meaning  of  Emf. — In  Section  2,  it  was  stated  that  one  of 
the  important  electrical  quantities  is  the  electromotive  force,  which 
is  the  cause  of  the  electric  current.  In  order  to  fix  in  mind  the 
ideas  underlying  the  electric  circuit,  it  will  be  helpful  to  consider 


F1Q.  (6 


some  illustrations  drawn  from  experiences  familiar  to  every  one. 
Assume  that  a  body  of  1  pound  weight  is  raised  from  the  floor  to  a 
table,  through  a  height  of  3  feet  (Fig.  16).  Work  is  done  upon  the 
body,  and  the  amount  of  work  done  is  given  by  1X3=3  ft.-lb. 
The  body  has  acquired  "potential  energy"  by  this  change  in  its 
position.  That  is,  it  is  capable  of  falling  back  to  the  floor  by  itself, 
and  in  falling  back  it  will,  when  brought  to  rest,  do  an  amount  of 
work  exactly  equal  to  that  which  was  done  in  lifting  it. 

The  difference  in  level  between  floor  and  table  may  be  expressed 
in  either  of  two  ways;  first,  in  the  ordinary  way,  by  stating  directly 
the  vertical  distance  through  which  the  body  was  raised;  and  second, 


RADIO  COMMUNICATION.  37 

by  stating  the  amount  of  work  required  to  carry  1  lb.  of  matter 
from  the  lower  to  the  higher  level.  This  difference  in  level,  then, 
defines  a  very  definite  difference  in  condition  between  the  two  posi- 
tions. The  higher  position,  considered  as  a  point  in  space,  has  a 
characteristic  which  distinguished  it  from  the  lower  position,  and 
that  is  the  amount  of  potential  energy  possessed  by  a  body  when 
placed  there.  In  other  words,  a  body  placed  at  this  point  is  able, 
by  virtue  of  its  position,  to  do  a  certain  amount  of  work.  If  we 
assume  that  the  body  has  unit  mass  this  characteristic  is  called  the 
gravitational  potential  of  the  point.  The  higher  position  is  said  to 
have  a  higher  potential  than  the  lower  position,  and  the  difference 
in  potential,  measured  in  terms  of  work,  is  a  measure  of  the  differ- 
ence in  height. 

Following  this  illustration  a  little  further,  we  may  consider  the 
case  of  a  simple  pump,  which  raises  water  from  a  level  St  to  some 
higher  level  S2  (Fig-  17).  The  water  raised  by  the  pump  to  the 
level  £2  possesses  potential  energy  or  energy  of  position.  That  is, 
it  is  able  to  fall  back  by  itself  to  the  lower  level,  and  in  falling 
back  it  will  do  an  amount  of  work  exactly  equal  to  that  which  was 
done  in  lifting  it.  Instead  of  measuring  the  difference  in  level  by 
the  height  h,  as  before,  it  may  be  measured  in  terms  of  the  work 
done  in  lifting  1  lb.  of  water  from  Si  to  S2.  This  difference  in 
level  may  be  called  the  difference  in  potential  between  /S^  and  S2. 

The  purpose  of  the  pump  is  to  transform  the  energy  supplied  by 
some  steam  engine  or  other  prime  mover  into  potential  energy,  with 
the  corresponding  difference  in  level  or  pressure  head.  This  estab- 
lishes what  might  be  called  a  watermotive  force,  which  causes  or 
tends  to  cause  a  flow  of  water  through  a  return  connecting  pipe. 

Coming  now  to  the  electrical  case,  let  us  consider  that  electric 
current  is  supplied  to  the  motors  of  an  electric  car  by  means  of  a 
generator  G,  Fig.  18,  and  two  conductors,  the  trolley  wire  and  the 
track.  Mechanical  energy  is  being  supplied  to  the  generator  by 
some  source  of  power,  such  as  a  steam  engine,  and  is  being  trans- 
formed into  electrical  energy.  This  transformation  results  in  a  flow 
of  current  as  indicated  by  the  arrows,  when  a  complete  circuit  is 
made  through  the  car  motors.  This  condition  is  described  by  saying 
that  there  is  a  difference  of  electric  potential  between  the  terminals 
of  the  generator,  or  between  the  trolley  wire  and  the  track.  It  is  the 
purpose  of  any  electric  generator  to  set  up  this  difference  of  potential 
between  its  terminals,  which  corresponds  to  the  difference  in  level 


38  RADIO    COMMUNICATION. 

of  the  water  in  the  earlier  illustrations.  Difference  of  electric  poten- 
tial is  then  a  difference  in  electric  condition  which  determines  the 
direction  of  flow  of  electricity  from  one  point  to  another. 

Just  as  height  of  water  column  or  difference  in  level  may  be 
regarded  as  establishing  a  pressure  or  watermotive  force,  which  in 
turn  causes  a  flow  of  water  when  the  valves  in  the  pipe  are  open,  so 
the  electric  potential  difference  may  be  regarded  as  establishing  an 
electromotive  force  which  causes  a  flow  of  electricity  when  a  con- 
ducting path  is  provided.  Electromotive  force  may  be  defined  as 
that  which  causes  or  tends  to  cause  an  electric  current. 

The  unit  of  electromotive  force  is  the  volt.  It  is  that  emf.  which  will 
cause  a  current  of  1  ampere  to  flow  through  a  resistance  of  1  ohm. 

The  relation  between  electromotive  force,  current,  and  resistance 
is  called  Ohm's  law.  This  law  is  discussed  further  in  the  next 
section. 

The  potential  difference  between  two  points  may  be  measured  in 
terms  of  the  work  done  in  conveying  a  unit  quantity  of  electricity 
from  one  point  to  the  other.  In  general 


~  Q 

where  E  is  in  volts,  Wis  in  joules  and  Q  is  in  coulombs.  (See  Appen- 
dix 2,  Units.  )  In  practice,  however,  it  is  measured  by  direct  applica- 
tion of  an  instrument  called  a  "voltmeter."  (See  Sec.  50.) 

14.  Ohm's  Law.  —  If  the  pressure  upon  a  pipe  line  is  increased, 
the  flow  of  water  through  it  in  gallons  per  minute  is  increased.  Ohm 
found  that  an  increase  in  the  emf.  applied  to  a  given  conductor 
caused  a  strictly  proportional  increase  in  the  current.  Doubling 
the  emf.  causes  exactly  twice  as  great  a  current  as  before,  trebling 
the  emf.,  three  times  as  great  a  current,  etc.  This  means  that  for  a 
given  conductor  the  ratio  of  emf.  to  current  is  a  constant,  and  this 
constant  has  been  called  the  resistance  of  the  conductor.  This 
important  relation  is  known  as  Ohm's  law,  and  may  be  written: 

f=*  (9) 

or,  in  the  alternative  forms, 

E=RI  (l(n 

and 

Hi  (ID 


RADIO   COMMUNICATION. 


39 


Ohm's  law  derives  its  great  importance  from  the  fact  that  it  applies 
to  each  separate  portion  of  an  electric  circuit  and  also  to  the  circuit 
as  a  whole. 

Case  I.  Ohm's  Law  for  a  Portion  of  a  Circuit. — Assume  some  part  of 
a  complete  circuit,  R,  Fig.  19,  which  is  held  at  a  constant  tempera- 
ture, and  has  no  battery  or  other  source  of  emf.  between  the  points 
A  and  B.  If  current  from  an  outside  source  is  then  caused  to  flow 
through  R,  and  correct  instruments  are  used  for  measuring  current 
and  voltage,  respectively,  the  following  data  may  be  taken,  showing 
that  R  has  a  value  of  2  ohms,  and  that  R  being  constant  the  current 
is  directly  proportional  to  the  voltage. 


R 
Ohms. 

E 
Volts. 

I 
Amperes. 

2 

1 
2 

4 
0 
8 
10 

f 

2 
3 
4 
5 

Suppose  two  straight  lines  OF  and  OX  are  drawn  at  right  angles  to 
each  other,  Fig.  20.  Divide  each  line  into  units  and  set  down  the 
proper  numbers  at  regular  intervals  along  these  two  lines.1  The 
numbers  on  the  0  Y  axis  may  be  used  to  represent  values  of  E,  and 
the  numbers  on  the  OX  axis  to  represent  values  of  /. 

At  a  point  1  on  the  E  axis  draw  a  light  line  parallel  to  the  0 X 
axis,  and  from  the  point  |  on  the  OX  axis  draw  a  light  line  parallel 
to  the  OY  axis.  Where  these  two  lines  intersect  make  a  dot.  Pro- 
ceed in  this  way  for  all  the  corresponding  values  of  E  and  I  in  the 
table  above,  and  then  connect  the  dots  by  a  line.  It  is  seen  that 
the  ratio  of  E  to  I  is  the  same  for  every  point  that  may  be  taken 
on  the  line  OP.  This  means  that  E  and  I  are  connected  by  a  con- 
stant factor  and  I  is  said  to  be  directly  proportional  to  E.  This 
process  is  called  plotting  the  relation  between  the  two  quantities 
E  and  I.  Proportionality  is  indicated  by  the  straightness  of  the 
plotted  line. 

Again,  assume  that  a  constant  voltage  E/  is  applied  across  the 
terminals  of  R,  Fig.  19.  By  some  suitable  means,  change  the 

1  These  lines  are  called  axes.  OY  is  called  the  axis  of  ordinatesand  OX  is  called 
the  axis  of  abscissas.  A  distance  measured  along  OY  is  called  an  ordinate.  A  dis- 
tance measured  along  OX  is  called  an  abscissa. 


40 


RADIO    COMMUNICATION. 


values  of  R  through  a  considerable  range.     The  following  are  some 
values  which  careful  observation  might  yield. 


E1 

Volts. 

R 
Ohms. 

/ 

Amperes. 

24 

2 
3 
4 
6 
8 
12 

12 
8 
6 
4 
3 
2 

Plot  the  values  of  R  and  7  on  cross-section  paper,  Fig.  21,  and 
the  curve  A  A  is  obtained. 

Also  we  may  plot  reciprocals  of  R  (values  of  I/R)  on  the  axis  of 
abscissas,  against  values  of  J  on  the  axis  of  ordinates,  Fig.  22.  It 


Voltmeter 


R. 

FIO.  19 


FlCUo 


Fia-zi 


is  now  seen  that  J  is  proportional  directly  to  the  reciprocal  of  R,  or 
in  other  words,  /is  inversely  proportional  to  72.  The  student  should 
make  some  experiments  of  this  sort  with  a  resistance  box,  battery, 
ammeter  and  voltmeter.  He  should  also  make  a  careful  record  of 
the  readings  taken,  and  then  should  plot  them  on  cross-section 
paper,  as  suggested  above.  From  such  a  study  it  will  be  found 
that: 


RADIO   COMMUNICATION.  41 

(a)  For  a  constant  resistance,  the  current  flowing  is  directly  pro- 
portional to  the  voltage. 

(6)  For  a  constant  voltage  the  current  is  inversely  proportional 
to  the  resistance. 

It  is  customary  to  speak  of  the  current  flowing  "in"  a  circuit;  of 
the  resistance  "of"  a  circuit  and  of  the  emf.  "between  the  termi- 
nals" of,  or  "across"  any  portion  of  a  circuit. 

The  relation  expressed  in  equation  (10)  applied  to  a  part  of  a  cir- 
cuit is  used  so  much  practically,  that  the  value  of  W  between  A  and 
B  (Fig.  19)  has  been  given  various  names.  It  is  called  (a)  the  RI 
drop,  (6)  the  potential  drop,  or  (c)  the  fall  of  potential  in  the  portion 
of  the  circuit  between  A  and  B.  If  a  branch  circuit  which  contains 
a  current  indicating  instrument,  such  as  a  voltmeter,  (Fig.  19)  is  con- 
nected between  these  two  points,  a  flow  of  current  is  shown  to  be 
taking  place.  The  point  A  is  at  a  higher  electric  potential  than  B, 
and  hence  current  will  flow  along  the  path  A  —  Vm  —  B. 

Case  II,  Ohm's  Law  for  a  Complete  Circuit.  —  In  extending  this  idea 
to  the  entire  circuit,  the  total  resistance  of  the  circuit  must  be  used. 
This  must  include  the  internal  resistance  of  the  generator  or  battery, 
or  the  sum  of  the  resistances  of  all  the  generators/  if  there  is  more  than 
one.  Likewise  the  voltage  must  be  the  resultant  or  algebraic  sum 
of  all  the  emfs.  in  the  circuit.  Ohm's  law  for  the  complete  circuit 
may  then  be  written  in  the  form  : 

E 
R 


In  this  equation  R  must  be  the  sum  of  all  the  resistances  in  circuit, 
including  the  resistances  of  all  the  batteries  or  generators.  In  the 
the  same  way  E  must  be  the  sum  of  all  the  emfs.  ,  each  with  its  proper 
sign.  For  example,  there  might  be  a  number  of  batteries  in  series 
(see  Sec.  24)  and  one  or  more  of  these  might  be  connected  into  the 
circuit  with  the  poles  reversed.  These  emfs.  would  have  to  be  sub- 
tracted, hence  the  negative  sign  for  the  terms  in  the  numerator. 

Another  way  of  stating  this  general  law  when  all  parts  of  the  cir- 
cuit are  in  series  is  to  equate  the  total  emf.  impressed  on  the  circuit 
to  the  sum  of  the  RI  drops  in  every  separate  portion  of  the  circuit, 

E=RI=RJ+R2I+R3I+  .....  (13) 

Ohm's  law  is  to  be  regarded  as  an  experimental  truth,  which  has 
been  established  by  countless  tests  for  all  metals  and  conducting 


42  RADIO    COMMUNICATION. 

liquids.  For  gases  at  low  pressures  it  does  not  hold,  nor  does  it 
apply  to  certain  non-conductors,  such  as  insulating  oils,  rubber,  and 
paraffin. 

15.  Sources  of  Emf. — There  are  a  number  of  ways  in  which  elec- 
tric energy  can  be  derived  from  other  forms  of  energy.  Each  one  of 
these  energy  transformations  sets  up  a  condition  which  causes  current 
to  flow,  that  is,  it  produces  an  emf.  The  principal  sources  of  emf. 
will  be  discussed  briefly  in  the  following  sections. 

Static  or  Fractional  Electricity. — When  a  piece  of  hard  rubber  is 
brought  into  close  contact  with  a  piece  of  cat's  fur  and  then  separated 
from  it,  two  things  may  be  noticed: 

1.  The  bodies  have  both  acquired  new  properties,  and  are  said  to 
be  electrified. 

2.  A  force  is  required  to  separate  the  bodies  and  work  is  done  if 
they  are  moved  apart. 

Both  bodies  now  have  the  power  of  attracting  light  bits  of  chaff 
or  tissue  paper.  The  rubber  is  said  to  have  a  negative  charge  and 
the  fur,  a  positive  charge.  These  charges  exist  in  equal  amounts 
and  taken  together  they  neutralize  each  other.  An  uncharged 
body  is  said  to  be  neutral.  When  these  charges  are  at  rest  upon  con- 
ductors they  are  called  electrostatic  charges.  Electric  charges  may 
be  communicated  to  small  light  bodies,  like  pith  balls,  and  if  these 
are  suspended  from  silk  threads  the  effects  and  properties  of  the 
charges  may  be  studied  in  terms  of  the  motions  and  behavior  of  the 
pith  balls.  Two  pith  balls  charged  oppositely  are  found  to  attract 
each  other,  and  two  with  like  charges  to  repel  each  other.  The 
force  between  them  in  either  case  is  proportional  to  the  product  of 
the  charges  and  inversely  proportional  to  the  square  of  the  distance 
between  them.  The  force  is  also  proportional  directly  to  the  value 
of  the  dielectric  constant.  (See  Sec.  31.) 

Electrostatic  forces  are  ordinarily  very  small.  There  are  many 
substances  other  than  the  two  mentioned,  which  become  charged  by 
friction  with  other  materials.  As  glass  is  such  a  substance,  the  glass 
face  of  an  instrument  should  never  be  wiped  with  a  cloth  just  pre- 
vious to  use,  as  it  thus  may  accidentally  become  charged  to  such 
an  extent  as  to  affect  the  light  needle  below  it  and  cause  a  consid. 
erable  error  in  its  reading.  In  case  this  has  happened,  breathing 
upon  the  glass  or  wiping  it  with  a  moist  cloth  will  remove  the  charge. 

If  two  bodies  carrying  opposite  charges  are  connected  by  a  con- 
ductor, a  momentary  flow  of  current  takes  place,  and  the  two  bodies 


RADIO   COMMUNICATION.  43 

come  to  the  same  electrical  condition.  If  the  original  charges 
were  equal,  both  bodies  are  discharged. 

Electrostatic  experiments  can  be  best  performed  on  a  cold  day 
when  the  air  is  dry.1 

Batteries. — When  two  plates  of  different  substances,  such  as  two- 
metals,  or  a  metal  and  carbon,  are  placed  in  a  water  solution  of  certain 
salts  or  acids,  there  is  found  to  be  a  difference  of  potential  between 
them.  If  the  exposed  parts  of  the  plates,  called  the  electrodes, 
are  connected  by  a  conductor,  current  will  flow.  The  following- 
list  contains  the  names  of  some  of  the  substances  which  are  used 
as  battery  electrodes.  The  order  of  the  arrangement  is  such  that 
when  any  two  are  taken,  current  will  flow  through  the  wire  from  the 
one  appearing  higher  in  the  list  to  the  one  farther  down: 

+  Carbon. 

Mercury. 

Copper. 

Iron. 

Lead. 

Cadmium. 

Tin. 

Zinc. 
—  Magnesium. 

The  salt  and  acid  solutions  used  are  conductors  of  electricity,, 
but  their  conductivity  is  not  so  high  as  that  of  the  metals.  They 
are  called  "  electrolytes. '  '2  Some  examples  are  solutions  of  sulphuric 
acid,  copper  sulphate,  potassium  chloride,  and  sodium  chloride 
or  common  salt.  Ordinary  water  from  the  service  pipes  contains 
enough  dissolved  substance  so  that  it  conducts  electricity  to  a, 
slight  extent.  With  any  two  materials  of  the  table  dipped  in  one 
of  the  solutions  mentioned,  there  will  be  produced  an  emf.  and  a 

1  For  further  study  of  electrostatic  phenomena  the  student  is  referred  to  Crew,, 
General  Physics,  Chap.  IX;  Franklin  and  MacNutt,  General  Physics,  Chap.  XV; 
Starling,  Electricity  and  Magnetism,  V;  S.  P.  Thompson,  Elementary  Lessons  in 
Electricity  and  Magnetism,  Index;  W.  H.  Timbie,  Elements  of  Electricity,  Chap, 
XI;  Watson,  A  Textbook  of  Physics,  pp.  633-680. 

2  Not  only  do  electrolytes  conduct  electricity,  but  when  a  current  is  passed  through 
them,  the  molecules  of  the  acid  or  of  the  salt  are  decomposed  or  broken  up.     The 
metallic  part  of  the  molecule,  or  its  hydrogen,  always  travels  toward  the  terminal 
from  which  the  current  leaves  the  solution,  and  is  deposited  there.     This  is  the 
basis  of  electroplating  processes,  and  it  is  in  terms  of  such  a  process  that  the  ampere 
was  denned.    (See  Sec.  5.) 


RADIO    COMMUNICATION. 


resulting  flow  of  current.    The  farther  apart  the  selected  materials 
stand  in  the  list  the  greater  will  be  the  effect  produced. 

This  arrangement  for  producing  a  current  is  called  a  "voltaic 
cell."  Several  types  of  this  cell  will  be  described  in  sections  17 
to  19. 

Thermoelectricity. — Assume  pieces  of  two  different  metals  CJ  and 
C"«7,  Fig.  23,  soldered  together  at  the  point  /.  The  other  ends  are 
connected  by  a  copper  wire  through  the  galvanometer  g.  If  the 
point  of  contact,  or  junction  /,  is  heated  to  a  temperature  above  that 

_        |    of  C  and  C",  there  will  be  a 

flow  of  current  through  the 
galvanometer.  This  is  com- 
monly explained  by  saying 
that  at  the  junction  /,  heat 
energy  is  transformed  into 
electrical  energy,  and  this 
junction  is  regarded  as  the 
seat  of  an  emf .  In  case  the 
temperature  of  /  is  lower 
than  that  of  CC",  the  direc- 
tion of  the  current  will  be 
reversed .  In  the  following 
table  some  common  metals 
are  so  arranged  that  when  any  two  of  them  are  chosen  for  the  cir- 
cuit, current  flows  across  the  heated  junction  from  any  one  to  one 
standing  lower  in  the  list. 

Bismuth. 

Platinum. 

Copper. 

Lead. 

Silver. 

Antimony. 

The  presence  at  the  junction  of  an  intermediate  metal  or  alloy 
like  solder,  will  not  affect  the  value  of  the  emf.  developed,  because 
whatever  effect  is  developed  at  one  point  of  contact  with  the  solder, 
is  annulled  at  the  other.  Of  the  pure  metals,  a  thermocouple  made 
of  bismuth  and  antimony  gives  the  greatest  thermoelectromotive 
force  for  a  given  difference  in  temperature.  However,  certain  alloys 
are  frequently  used  for  one  or  both  of  the  materials.  The  purity  and 


Thermo - 
Junction 


no.  23 


RADIO  COMMUNICATION.  45 

physical  state  of  these  materials  is  an  important  factor  in  securing 
uniformity  of  results.  A  thermoelement  or  thermocouple  may  be 
calibrated  with  a  given  galvanometer;  that  is,  a  curve  may  be 
plotted  coordinating  microvolts  and  temperatures.  It  then  becomes 
a  valuable  device  for  measuring  temperatures,  especially  where 
other  forms  of  thermometer  cannot  be  used.  For  the  range  from 
liquid  air  temperatures,  -190°  C.,  to  200°  or  300°  C.,  copper-advance 
or  iron-advance  thermocouples  are  often  used.  For  high  tempera- 
tures, upward  of  1700°  C.,  a  thermocouple  of  platinum  and  a  plati- 
num-rhodium alloy  is  used. 

Thermocouples  find  application  in  radio  measurements  in  hot 
wire  ammeters.  See  Section  59. 

Induced  Emf. — Electromotive  force  may  be  set  up  in  a  circuit  by 
the  expenditure  of  mechanical  work  in  pushing  wire  conductors 
across  magnetic  lines  of  force.  See  Section  45.  Also  when  electric 
current  in  any  circuit  is  caused  to  vary,  an  emf .  which  is  the  result 
of  this  variation  arises  in  a  nearby  circuit.  The  principles  which 
apply  to  these  cases  are  fully  stated  in  Sections  45  and  47.  The 
development  of  machinery  based  upon  these  principles  is  the  sub- 
ject of  Chapter  2. 

The  RI  Drop. — When  for  some  purpose  a  voltage  is  desired  which 
is  less  than  that  of  the  available  battery  or  generator,  or  one  which 
can  be  readily  adjusted  to  any  desired  value,  it  is  often  convenient 
to  take  advantage  of  the  RI  drop  across  a  given  resistance,  as  de- 
scribed in  Section  14,  and  to  arrange  a  circuit  as  in  Fig.  24.  The 
current  from  the  battery  which  flows  through  the  resistance  ab  can 
be  adjusted  to  any  desired  value  by  properly  choosing  the  value  of 
ab. 

Since  the  voltage  drop  along  ab  is  directly  proportional  to  the 

resistance  r,  any  desired  fraction,  —  E'  may  be  obtained  by  setting 

the  contact  c  at  such  a  point  that  the  resistance  ac  is  equal  to  —  r.   This 

follows  from  equation  (10)  where  it  is  seen  that  the  emf.  across  any 
resistance  is  directly  proportional  to  that  resistance  so  long  as  the 
current  remains  constant.  This  is  nearly  enough  true  for  practical 
purposes  if  it  be  assumed  that  the  resistance  of  ab  is  relatively  large 
as  compared  to  the  internal  resistance  of  the  battery.  The  resist- 
ance ab  may  be  in  the  form  of  a  resistance  box  with  a  travelling 
contact  at  c,  or  it  may  be  a  uniform  homogenous  wire,  with  an 
adjustable  contact  point  at  c.  Such  a  device  for  subdividing  a 


46 


RADIO    COMMUNICATION. 


voltage  is  called  a  "voltage  divider,"  and  has  often  been  erroneous- 
ly called  a  potentiometer. 

Standard  of  Electromotive  Force. — The  emfs.  due  to  the  ordinary 
battery  cells  are  usually  between  1  and  2  volts.  A  certain  type  of 
cell  has  been  selected  by  international  agreement  as  a  standard  of 
emf.  The  type  now  most  used  is  called  the  Weston  standard  cell, 
because  it  was  first  suggested  by  Weston.  It  is  also  called  the  '  'cad- 
mium cell,"  because  cadmium  is  used  as  the  negative  electrode. 
This  cell  is  made  from  carefully  selected  chemicals  of  great  purity, 
and  when  used  under  controlled  temperature  conditions  its  voltage 
can  be  depended  upon  to  remain  constant  within  a  few  parts  in 


Line 


\ 


F)G. 


100,000.  At  20°  C.,  its  emf.  is  1.0183.  The  value  of  the  volt  is 
maintained  by  reference  to  similar  cells  kept  in  the  national 
standardizing  laboratories. 

16.  Internal  Voltage  Drop  and  Line  Drop. — Reference  to  equation 
(12),  page  41,  will  show  that  the  voltage  or  emf.  of  the  generator, 
whether  battery  or  dynamo,  must  always  be  thought  of  as  being 
expended  in  three  parts,  as  follows: 

1.  That  part  which  sends  current  through  the  generator  itself, 
called  the  "internal  drop." 

2.  That  part  which  sends  current  through  the  line,  called  the 
"line  drop." 


RADIO   COMMUNICATION.  47 

3.  That  part  which  sends  current  through  the  terminal  apparatus, 
such  as  lamps,  motors,  or  heating  coils.  This  is  the  useful  part  of 
the  emf.,  the  first  two  being  wasted  so  far  as  useful  work  is  concerned. 

This  division  of  the  generated  emf.  is  illustrated  in  Fig.  25.  Since 
part  3  is  the  part  which  is  applied  in  the  external  circuit,  it  is  clear  that 
the  generator  must  always  supply  a  higher  voltage  than  is  needed 
at  the  terminals  in  order  to  take  care  of  parts  1  and  2.  The  above 
facts  may  be  again  stated  in  the  form 

Total  emf.=drop  in  generator  -f  drop  in  line+useful  drop  in  load. 

Voltage  Drop  in  Battery  or  Generator.  —  Assume  a  circuit  as  shown 
in  Fig.  26.  As  long  as  the  key  K  is  open,  the  battery  is  not  sending 
current  through  the  circuit  R.  A  high  resistance  voltmeter  Vm 
gives  a  reading  E  which  is  the  full  open  circuit  voltage  of  the  cell. 
The  voltmeter  current  is  so  small  that  the  cell  may  be  regarded  as 
supplying  no  current  through  it.  If,  without  removing  the  volt- 
meter, the  key  K  is  closed  ,  a  current  /  flows  through  the  external 
circuit  R,  and  the  voltmeter  reading  is  seen  to  drop  back  to  some 
value  E'  which  is  less  than  E.  As  R  is  made  smaller  the  value 
of  W  continues  to  decrease,  until  when  R=0,  that  is  when  the  poles 
of  the  cell  are  short-circuited,  the  voltmeter  shows  no  deflection 
whatever.  The  voltmeter  indicates  at  any  instance  the  then  existing 
value  of  the  voltage  at  the  cell  terminals  and  this  may  vary  from  the 
open  circuit  voltage  or  emf.  E,  to  zero,  depending  upon  the  external 
circuit  condition.  For  any  value  of  R  the  current  flowing  is  given 
by  the  equation 


where  r  is  the  internal  resistance  of  the  cell,  or 

E=RI+rI  (15) 

Thus  the  emf.  E,  is  equal  to  the  sum  of  the  potential  drop  in  the  cell 
and  the  RI  drop  in  the  external  circuit.  Denoting  RI  by  E',  we 
may  write  equation  (15)  in  the  form 

E'=E-rI  (16) 

The  quantity  E'  is  called  the  ''terminal  potential  difference,"  or 
the  "terminal  voltage"  of  the  cell,  and  it  is  always  less  than  the  full 
emf.  by  the  RI  drop  in  the  cell  itself.  It  may  be  defined  as  the 
useful  part  of  the  emf.,  or  that  part  which  is  available  for  sending 
current  through  the  external  circuit. 


48  RADIO    COMMUNICATION. 

The  emf .  E  is  determined  once  for  all  by  the  choice  of  materials 
used  in  the  cell,  and  it  can  not  be  in  any  way  altered  after  the  cell 
is  once  chosen.  The  terminal  voltage  however  can  be  varied 
through  all  possible  values  from  E  to  zero.  Anything  that  may  be 
done  to  lessen  the  internal  resistance  of  the  battery,  such  as  putting 
several  cells  in  parallel  (see  Sec.  24),  will  lower  the  RI  drop  and 
correspondingly  increase  the  terminal  voltage  E'.  After  the  RI 
drop  has  been  subtracted  from  the  emf.  E,  the  balance  is  the  terminal 
voltage,  or  that  part  of  the  emf.  which  is  available  for  work  in  the 
external  circuit.  The  current  drawn  from  the  battery  must  be 
regarded  as  flowing  through  the  entire  circuit.  As  this  value  of  J 
increases,  the  internal  voltage  drop  in  the  battery  increases,  and  a 
correspondingly  smaller  fraction  of  the  total  emf.  is  available  for 
the  external  circuit. 

What  has  been  said  here  of  a  cell  is  equally  true  of  any  other 
form  of  generator. 

Voltage  Drop  in  the  Line. — Suppose  that  a  d.c.  generator,  capable 
of  supplying  115  volts  at  the  outgoing  wires  of  a  powerhouse  is 
furnishing  current  to  a  distant  building  for  lighting  lamps  which 
require  110  volts.  Suppose  that  the  line  resistance  is  0.1  ohm  and 
that  the  lamps  require  50  amp.  of  current.  There  is  then  a  line 
drop  of  5  volts,  and  the  available  voltage  at  the  generator  is  just 
right  to  operate  the  lamps  at  their  rated  voltage.  Suppose,  how- 
ever, that  other  apparatus  near  the  lamps,  say,  the  motor  of  an 
electric  elevator,  is  put  in  operation,  and  that  this  requires  100 
amp.  of  current.  The  line  drop  is  then  increased  by  10  volts, 
or  15  volts  in  all,  and  the  voltage  available  at  the  distant  end  of  the 
line  has  fallen  to  100  volts.  This  is  not  enough  to  maintain  the 
lamps  at  full  brightness  and  they  are  dimmed  perceptibly  every 
time  the  elevator  is  operated.  To  correct  this  difficulty,  a  new  line 
of  lower  resistance  must  replace  the  old  one;  that  is,  the  line  drop 
must  be  decreased,  so  that  for  the  maximum  current  demand  the 
lamps  will  not  fall  below  110  volts.1 

Another  example  of  the  line  drop  is  seen  in  the  dimming  of  the 
lights  of  a  trolley  car  when  the  car  is  starting.  The  resistance  of  the 
trolley  wire  is  kept  low  by  using  a  large  cross  section  of  copper,  and 
the  track  resistance  is  kept  as  low  as  possible  by  careful  bonding  at 

*  Problem—  Assuming  that  the  distance  from  powerhouse  to  lamps  is  \  mile,  cal- 
culate the  resistance  of  the  line  which  is  necessary  to  maintain  the  lamp  voltage 
at  110  volts.  Find  also  the  size  of  copper  wire  which  should  be  used  for  this  line. 


RADIO  COMMUNICATION.  49 

the  rail  joints.  However,  a  few  defective  joints  raises  the  track 
resistance  and  increases  the  line  drop  to  such  a  degree  that  the 
necessary  lamp  voltage  cannot  be  maintained  when  the  car  starts. 

D.  Batteries. 

17.  Kinds  of  Cells. — An  electric  battery  is  made  up  of  a  group  of 
cells  so  arranged  as  to  produce  a  greater  effect  than  one  alone.     The 
term  "battery"  is  sometimes  incorrectly  used  to  mean  one  such 
cell.     We  have  seen  that  the  cell  is  a  device  for  converting  chemical 
energy  into  electrical  energy.     There  are  two  principal  types  of 
cells.     One,  in  which  the  action  can  only  be  renewed  by  putting  in 
new  chemicals  or  parts,  is  called  a  "primary"  cell.     In  the  other 
type  of  cell  the  necessary  chemicals  can  be  renewed  by  a  charging 
process;  i.  e.,  sending  current  through  the  cell  in  a  direction  oppo- 
site to  that  which  the  cell  itself  produces.     Such  cells  are  called 
"'secondary"  or  "storage"  cells.     They  can  be  used  over  and  over 
again  without  putting  in  fresh  chemicals.     A  group  of  these  is 
commonly  called  a  storage  battery.     These  will  be  discussed  more 
fully  in  Section  21. 

18.  Simple  Primary  Cell. — If  a  plate  of  pure  zinc  and  a  plate  of 
copper,  not  in  contact  with  each  other,  are  immersed  in  dilute 
sulphuric  acid,  no  chemical  action  takes  place.     When  the  plates 
are  connected  by  a  wire  or  other  conductor  outside  of  the  liquid  a 
current  flows  in  the  wire  and  a  chemical  action  occurs  in  the  cell. 
The  sulphuric  acid  attacks  the  zinc,  forming  zinc  sulphate,  and  the 
hydrogen  liberated  from  the  acid  appears  at  the  copper  plate.     The 
direction  of  the  current  flow  is  from  the  copper  plate  out  around  the 
metallic  circuit  to  the  zinc  plate  and  then  back  through  the  acid  to 
the  copper  plate.     The  direction  of  this  current  in  the  external 
circuit  is  arbitrarily  said  to  be  from  the  copper  or  positive  plate  to 
the  zinc  or  negative  plate.     In  diagrams,  such  as  Fig.  27,  p.  50,  the 
positive  plate  is  indicated  by  a  plus  sign  (  +  ),  and  the  negative 
plate  is  indicated  by  a  negative  sign  (  — ).     If  an  ammeter  or  volt- 
meter is  connected  into  the  circuit  its  positive  terminal  is  connected 
to  the  positive  plate  of  the  cell. 

Every  primary  cell  has  two  plates,  called  "electrodes"  or  poles, 
and  a  liquid  called  the  "electrolyte."  The  electrodes  are  metals 
or  carbon,  and  the  two  electrodes  cannot  be  the  same  substance. 
Among  the  commonly  used  electrolytes  are  solutions  of  sulphuric 
acid,  copper  sulphate,  ammonium  chloride,  and  other  chlorides. 
97340° — 19 4 


50 


RADIO    COMMUNICATION. 


The  voltage  given  by  the  usual  cells  is  between  1  and  2  volts  per 
cell.  The  voltage  of  a  cell  depends  mainly  upon  the  pair  of  sub- 
stances used  as  electrodes,  and  is  affected  somewhat  also  by  the 
electrolyte.  Thus,  a  great  many  different  electrolytes  are  used  to 
make  up  cells  with  copper  and  zinc  as  electrodes,  but  all  give  close 
to  1  volt  per  cell.  This  fact  is  often  very  useful  when  a  certain 
voltage  is  wanted  and  no  regular  source  is  available.  By  taking 
two  different  metals  and  placing  them  in  any  acid  which  does  not 
attack  them  violently,  or  even  in  water,  an  emergency  source  of 
voltage  can  often  be  secured. 

Local  Action. — When  a  piece  of  pure  zinc  is  placed  in  a  solution  of 
sulphuric  acid,  no  action  is  observed  to  take  place  and  no  hydrogen 
is  evolved.  When  the  plate  of  zinc  contains  impurities,  however, 
such  as  particles  of  iron  or  carbon,  a  considerable  action  with  the 


evolution  of  hydrogen  is  noticed  as  soon  as  the  zinc  is  put  into  the 
acid.  The  reason  for  this  is  that  each  particle  of  a  foreign  substance 
in  the  surface  of  the  zinc  acts  with  a  neighboring  particle  of  zinc  as  a 
voltaic  cell,  and  the  effect  is  that  of  a  number  of  tiny  cells,  all 
exhausting  themselves  in  producing  local  currents  which  are  purely 
wasteful.  This  sort  of  local  action  in  the  ordinary  cell  contributes 
nothing  to  the  useful  energy  output  of  the  cell. 

Polarization. — The  current  given  by  the  simple  cell  described 
above  does  not  remain  constant,  but  begins  to  diminish  soon  after 
the  circuit  is  closed.  The  hydrogen  which  is  liberated  from  the  acid, 
when  current  flows,  accumulates  in  the  form  of  small  bubbles  on 
the  copper  plate.  It  thus  diminishes  the  area  of  contact  of  the  liquid 
with  the  copper,  and  so  increases  the  resistance  in  the  cell.  The 
presence  of  the  hydrogen  furthermore  diminishes  the  voltage  gener- 


RADIO   COMMUNICATION.  51 

ated  in  the  cell.  Both  the  reduction  of  the  generated  voltage  and 
the  increase  of  resistance  decrease  the  current  given  by  the  cell. 
This  behavior  caused  by  the  hydrogen  is  called  polarization.  The 
effect  disappears  a  while  after  the  circuit  is  opened,  by  gradual  dif- 
fusion of  the  hydrogen  away  from  the  copper  surface.  Polarization 
may  be  prevented  by  placing  some  substance  around  the  copper 
plate  to  remove  the  hydrogen  or  prevent  its  formation.  It  is  for  this 
reason  that  primary  cells  contain  a  chemical  substance  called  the 
"depolarizer"  in  addition  to  the  electrolyte. 

The  action  of  the  depolarizer  is  limited  to  the  positive  plate, 
and  it  is  kept  from  contact  with  the  negative  plate  in  various 
ways.  In  the  "gravity  cell,  "  one  of  the  forms  of  Daniell  cell  men- 
tioned in  the  table  just  below,  the  depolarizer  is  copper  sulphate 
solution,  which  is  kept  separate  from  the  electrolyte  by  the  action  of 
gravity.  Being  denser  than  the  electrolyte,  it  remains  at  the  bottom 
of  the  vessel.  The  copper  is  placed  at  the  bottom,  in  the  depelarizer, 
and  the  zinc  is  placed  at  the  top  in  the  electrolyte.  Another  method 
of  keeping  the  depolarizer  away  from  the  negative  electrode  is  by 
the  use  of  a  porous  cup  or  partition,  through  which  the  current  can 
pass,  but  the  liquids  can  diffuse  only  with  difficulty.  This  may  be 
of  paper,  cloth,  or  porous  porcelain. 

Characteristics  of  Good  Primary  Cells. — For  best  results  a  battery 
cell  is  usually  desired  which  has  as  large  an  emf.  as  possible.  This 
depends  upon  what  materials  are  chosen  for  the  plates,  but  not  at 
all  upon  their  size  or  arrangement.  If  a  large  current  output  is 
desired,  the  internal  resistance  of  the  cell  must  be  low.  This  de- 
pends upon  the  electrolyte  chosen,  and  also  upon  the  size  and 
arrangement  of  the  plates.  Large  plates,  close  together,  set  in  an 
electrolyte  of  low  volume  resistivity  are  the  conditions  necessary 
for  low  internal  resistance.  Constant  emf.  is  only  possible  if  the  cell 
is  free  from  polarization.  Economy  in  operation  depends  on  low 
first  cost  of  materials  and  freedom  from  waste  due  to  local  action. 
The  operation  of  the  battery  should  not  yield  disagreeable  or  poi- 
sonous fumes.  Dry  cells,  such  as  are  described  below,  have  all  of 
the  desirable  characteristics  here  mentioned  except  that  they  do 
polarize. 

19.  Types  of  Primary  Cells. 

Closed  Circuit  Cells. — Cells  which  are  used  with  the  electrical 
circuit  closed  for  fairly  long  periods  of  time  must  be  particularly 
free  from  polarization;  i.  e.,  the  cell  must  have  an  effective  depolar- 


52 


RADIO    COMMUNICATION. 


izer  around  the  positive  plate  to  prevent  hydrogen  from  collecting 
on  it.  The  make-up,  generated  voltage  and  approximate  resistance 
of  typical  cells  are  given  in  the  following  table. 


Name. 

Positive 
elec- 
trode. 

Nega- 
tive 
elec- 
trode. 

Electrolyte. 

Depolari/.er. 

Volts. 

Inter- 
nal re- 
sist- 
ance, 
ohms. 

Daniell..  .  . 

Copper 

Zinc 

Sulphuric  acid 

Copper  s  ul- 

1.1 

1 

Chromic  acid  

Edison-Lalande  . 
Silver  chloride... 

Carbon. 

Copper. 
Silver.. 

Zinc.. 

Zinc.. 
Zinc.. 

Sulphuric  acid. 

Caustic  potash. 
Ammonium 
chloride. 

phate. 
Chromium  pe- 
roxide. 
Copper  oxide... 
Silver  chloride  . 

2.0 

0.8 
1.0 

0.2 

0.03 
2 

The  silver  chloride  cell  is  classed  as  a  dry  cell,  being  made  in 
such  a  way  that  the  electrolyte  cannot  spill.  This  cell  will  last  a 
much  longer  time  than  the  more  common  kind  of  dry  cell  described 
below. 

Cells  for  Intermittent  Service. — For  service  such  as  ringing  door 
bells,  operating  telephone  buzzers,  and  ignition  devices,  a  primary 
cell  may  be  used  which  does  not  have  a  powerful  depolarizer.  The 
cell  can  recuperate  from  polarization  during  the  intervals  of  rest 
with  the  aid  of  only  a  slow  acting  depolarizer.  The  cell  universally 
used  for  such  service  is  the  sal  ammoniac  cell,  having  carbon  as  the 
positive  and  zinc  as  the  negative  electrode,  ammonium  chloride 
(sal  ammoniac)  as  the  electrolyte,  and  manganese  dioxide  as  the 
depolarizer.  The  voltage  generated  is  about  1.5  volts. 

20.  Dry  Cells. — The  sal  ammoniac  cell  is  now  used  almost  uni- 
versally in  the  form  of  the  so-called  dry  cell.  The  solution  of  sal 
ammoniac  is  contained  in  an  absorbent  material  and  the  cell  is 
thoroughly  sealed,  so  that  spilling  is  impossible. 

The  zinc  serves  as  the  container  for  the  cell,  being  a  can  made  of 
sheet  zinc  about  0.045  cm.  (0.018  in.)  thick.  The  positive  electrode 
is  a  large  rod  of  carbon  in  the  center  of  the  cell,  and  this  is  surrounded 
by  a  mixture  of  manganese  dioxide  and  carbon.  This  mixture, 
saturated  with  the  sal  ammoniac  solution,  is  bulky  and  occupies 
most  of  the  interior  of  the  cell.  The  electrolyte,  sal  ammoniac 
solution,  is  contained  partly  in  the  mass  of  depolarizing  mixture  and 
partly  in  the  porous  separator  that  is  placed  between  the  zinc  and  the 
depolarizer.  The  separator  is  usually  a  thick  pulpboard  in  large 


RADIO   COMMUNICATION.  53 

American  cells.  In  small  cells  and  nearly  all  European  cells  it  is  a 
cloth  bag,  spaced  in  from  the  zinc  so  that  it  is  surrounded  by  some  of 
the  electrolyte  in  the  form  of  a  paste. 

The  standard  dry  cell,  called  "No.  6,"  is  15  cm.  (6  in.)  high  by 
6.5  cm.  (2.5  in.)  in  diameter  and  weighs  about  900  grams  (2  lb.). 
There  are  two  principal  classes  of  these  cells — ignition  cells  for  heavy 
service  and  telephone  cells  for  light  and  intermittent  service.  There 
is  also  an  intermediate  cell  for  general  service,  having  characteristics 
between  these  two.  The  ignition  cells  deliver  an  instantaneous 
current  of  about  30  amp.  when  short  circuited,  provided  they  are 
new  and  little  used.  They  lose  their  energy  and  become  useless  in 
about  six  months.  The  telephone  cells  give  about  20  amp.  on  a 
momentary  short  circuit.  They  last  longer  than  the  cells  made  for 
heavy  service,  the  usual  life  being  about  a  year. 

Miniature  dry  cells,  used  for  flash  lights  and  for  plate  batteries  for 
low  power  vacuum  tubes,  are  made  in  sizes  varying  from  4  to  10  cm. 
in  height,  weighing  from  14  to  100  grams.  They  maintain  their 
effectiveness  only  a  few  months. 

The  voltage  generated  in  an  unused  dry  cell  is  from  1.5  to  1.65 
volts.  An  emf.  lower  than  1.45  volts  in  a  new  cell  indicates  dete- 
rioration or  defect.  However,  when  a  current  is  being  drawn  from 
a  cell,  the  voltage  at  its  terminals  is  less  because  part  of  the  generated 
voltage  is  used  in  overcoming  the  internal  resistance  of  the  cell. 
(See  Sec.  16.) 

The  standard  size  No.  6  dry  cells  give  a  total  of  about  25  watt- 
hours  ,of  energy.  The  amount  delivered  increases  somewhat  with 
increasing  temperatures.  The  higher  the  temperature,  however, 
the  faster  does  the  cell  deteriorate  when  not  in  use.  It  is  usually 
best  therefore  to  keep  dry  cells  at  a  temperature  below  25°  C.1 

The  dry  battery  is  chiefly  useful  for  supplying  (a)  relatively  large 
current  for  a  brief  instant  or  (6)  very  small  current  for  a  long  time. 
Owing  to  its  rapid  polarization,  the  dry  cell  is  not  able  to  deliver  a 
steady  current  for  a  long  time  in  service,  such  as  operating  lamps  or 
motors.  The  storage  battery  is  much  better  adapted  to  this  kind  of 
service. 

21.  Storage  Cells.2 — The  essential  difference  between  the  primary 
cell  previously  described  and  the  secondary  or  storage  cell  is  in  the 

1  For  further  information  on  dry  cells,  see  Circular  of  the  Bureau  of  Standards  No. 
79,  Dry  Cells,  1918;  Trans.  Amer.  Electrochem.  Soc.,  21,  p.  275, 1912;  Electrician,  69, 
p.  6,  1912;  71,  p.  481,  1913. 

2  See  also  S.  C.  Radio  Pamphlet  No.  8. 


54  RADIO    COMMUNICATION. 

manner  of  renewing  the  active  material  of  the  plates.  When  the 
primary  cell  is  exhausted,  it  is  renewed  by  renewing  the  electrolyte 
and  removing  the  worn  out  zinc  plate  and  putting  a  fresh  one  in 
its  place.  Dry  cells  cannot  be  so  renewed.  In  the  storage  battery, 
however,  the  necessary  chemical  condition  of  the  plates  is  restored 
by  the  action  of  a  current  from  an  outside  source.  The  direction  of 
this  current  is  opposite  to  that  of  the  current  supplied  by  the  cell. 
While  the  cell  is  giving  out  current,  it  is  said  to  be  discharging. 
While  it  is  receiving  current  from  some  outside  source,  it  is  said  to 
be  charging.  In  Fig.  28,  p.  50,  is  shown  a  typical  circuit  for  charging 
storage  cells.  The  dynamo  D  is  connected  through  the  ammeter  and 
rheostat  R  to  the  battery,  so  that  the  positive  pole  of  the  dynamo  is 
connected  to  the  positive  pole  of  the  battery,  thus  sending  the 
charging  current  against  the  emf.  of  the  battery.  This  is  very 
important.  A  mistake  in  connection  may  cause  permanent  injury 
to  the  battery.  Storage  batteries  in  general  have  low  internal 
resistances,  and  hence  they  will  yield  relatively  large  currents. 
Although  this  is  an  advantage,  there  is  also  the  danger  of  excessive 
currents  in  case  of  an  accidental  short  circuit.  Voltage  changes 
throughout  the  period  of  discharge  are  small,  and  so  fairly  constant 
currents  can  be  maintained.  There  are  two  types  of  storage  cell 
in  common  use:  (a)  the  lead  plate,  acid  electrolyte  cell;  (6)  the  nickel, 
iron  plate,  alkaline  electrolyte  cell.  Each  of  these  will  be  described 
in  the  following  sections. 

The  Lead  Plate,  Add  Electrolyte  Cell— In  this  type  of  cell  (Fig.  29) 
the  plates  are  made  of  lead,  and  contain  many  apertures,  so  that 
either  plate  is  sometimes  called  a  "grid.  "  Into  these  holes  in  the 
plate  there  is  forced,  by  heavy  pressure,  a  paste  made  by  mixing 
certain  lead  salts  (red  lead,  Pb304  and  litharge,  PbO)  with  sulphuric 
acid.  If  two  plates  thus  prepared  are  immersed  in  a  20  per  cent 
solution  of  sulphuric  acid,  and  if  an  electric  current  is  passed  between 
them,  hydrogen  will  accumulate  at  the  pole  from  which  the  current 
leaves  the  cell.  This  hydrogen  reduces  the  paste  to  spongy  lead. 
In  the  meantime  oxygen  is  being  taken  up  by  the  other  plate  and 
the  paste  is  being  changed  here  to  a  higher  oxide  (lead  peroxide, 
Pb02) .  The  cell  now  really  contains  a  lead  peroxide  plate  (positive) 
and  a  spongy  lead  plate  (negative).  These  materials  in  a  solution 
of  sulphuric  acid  yield  at  first  on  open  circuit  an  emf.  of  about  2.2 
volts.  This  quickly  drops  to  about  2  volts. 


RADIO  COMMUNICATION. 


55 


After  the  charging  current  is  cut  off,  if  the  cell  is  connected  to  a 
circuit,  current  will  flow  from  the  cell  in  a  direction  opposite  to 
that  of  the  charging  current.  As  the  discharge  goes  on,  the  voltage 
gradually  falls.  The  discharge  should  never  be  carried  beyond  the 
point  at  which  the  open  circuit  voltage  is  T.75. 

Lead  plate  batteries  are  usually  arranged  with  one  more  negative 
than  positive  plate.  The  container  must  be  made  from  a  material 


Alternate  J»ositiv|  | 
and  ne^tive  leaJ     R 
Plates  I1  £ 


Fiq.Z9 


which  the  acid  will  not  attack,  such  as  glass  or  hard  rubber.  The 
negative  plates  will  be  a  dark  gray  color,  and  the  positive  plates  will 
be  a  reddish  brown.  The  chemical  changes  in  charge  and  discharge 
require  time,  and  the  processes  can  not  be  unduly  hastened  without 
injury  to  the  cell.  The  manufacturer  always  specifies  in  amperes 
the  normal  rate  of  charge  or  discharge,  and  the  life  and  efficiency 
of  the  cell  are  greatly  decreased  if  this  normal  rate  is  disregarded. 


56 


RADIO    COMMUNICATION. 


There  is  a  chemical  combination  between  the  sulphuric  acid  and 
the  lead,  which  results  in  the  formation  of  lead  sulphate  during  the 
process  of  discharge.  This  uses  up  acid  and  during  this  time  the 
density  of  the  electrolyte  grows  less.  When  the  cell  is  again  charged, 
sulphuric  acid  is  returned  to  the  solution,  and  the  density  rises. 
For  testing  density  of  battery  solutions  an  instrument  called  the 
" hydrometer"  is  used.  The  density  of  the  electrolyte  is  the  best 
indication  of  the  condition  of  charge  or  discharge  of  the  cell.  The 
manufacturers  will  furnish  with  the  cells,  information  as  to  the 
•correct  values  of  the  density.  The  lead  sulphate  is  grayish  white 
in  color.  It  is  insoluble  in  sulphuric  acid  and  is  a  non-conductor  of 
-electricity.  It  should  be  entirely  reconverted  into  lead  when  the 
•cell  is  charged.  If  the  cell  is  repeatedly  charged  or  discharged  at 
the  normal  current  rate,  the  amount  of  lead  sulphate  formed  will  be 
small  and  not  essentially  harmful.  However,  charging  or  dis- 
charging at  an  excessive  rate,  or  allowing  the  cell  to  remain  idle  in  a 
discharged  condition,  will  cause  an  excessive  deposit  of  lead  sulphate 
and  the  plates  are  then  said  to  be  "sulphated."  The  growth  of  the 
crystals  of  the  sulphate  sets  up  stresses  which  tend  to  buckle  the 
plates  and  crowd  out  the  active  material,  thus  hastening  disintegra- 
tion. The  presence  of  the  non-conducting  coating  also  practically 
cuts  off  the  parts  of  the  plate  thus  covered  and  reduces  the  capacity 
of  the  cell.  The  condition  is  difficult  to  remove,  and  it  can  only  be 
prevented  by  a  careful  following  of  the  manufacturers'  rules  for 
charging,  discharging,  and  care.  During  the  charge,  hydrogen  is 
given  off  which  forms  an  explosive  mixture  with  the  air.  An  open 
flame  should  therefore  not  be  brought  near  the  cells  while  they  are 
charging. 

It  has  been  mentioned  that  there  is  a  certain  charge  or  discharge 
rate  specified  by  the  manufacturer,  which  is  most  favorable  for  each 
size  and  type  of  cell.  As  the  size  of  the  plates  increases,  larger 
charge  and  discharge  currents  may  be  used.  The  capacity  of  a 
storage  battery  is  rated  in  terms  of  ' '  ampere-hours, ' '  abbreviated  as 
"amp-hr."  For  example,  a  40-amp-hr.  cell  might  yield  1  amp.  for 
40  hours,  or  10  amp.  for  4  hours.  However,  if  5  amp.  is  the  normal 
discharge  rate  for  this  cell,  it  should  not  be  charged  nor  discharged 
at  a  greater  rate,  and  5  amp.  for  8  hours  represents  the  correct  con- 
ditions. 

The  ampere-hour  capacity  depends  upon  the  size  of  the  plates, 
and  upon  the  depth  of  the  active  material.  The  efficiency  of  either 
type  of  storage  cell  is  expressed  in  terms  of  ampere-hours  per  pound 


RADIO   COMMUNICATION. 


57 


weight  of  cell.  This  is  found  to  oe  not  very  different  for  the  two 
types,  provided  that  both  have  been  given  correct  care  and  regular 
and  careful  treatment.  The  student  should  be  especially  warned 
against  directly  short-circuiting  a  lead  cell.  Owing  to  its  low 
resistance,  dangerously  large  currents  may  flow,  also  it  is  certain  to 
injure  the  cell. 

The  Nickel-Iron  Plate,  Alkaline  Electrolyte  Cell. — In  this  type  of 
storage  cell,  Fig.  30,  developed  by  Edison,  the  positive  plate  con- 
sists of  alternate  layers  of  nickel  hydrate  and  'pure  nickel  flake, 


Valve 


Positive  |>ole 


Weld    tb  cover 

washer 

Connecting  rod 
Positive  &rid 
Qrid    se janitor 
Seamless  •steel  rinia 

Positive  1"ub«j 


cell  bottom 


packed  in  perforated  nickel  plated  steel  tubes.  Several  of  these 
are  mounted  side  by  side  in  a  steel  frame.  The  negative  plate 
consists  of  iron  oxide  held  in  a  somewhat  similar  way.  These 
plates  are  immersed  in  a  20  per  cent  solution  of  caustic  potash  in 
water,  and  the  whole  is  sealed  into  a  welded  sheet  steel  container. 
The  electrolyte  acts  only  as  a  carrier  of  oxygen  between  the  plates 
and  does  not  form  chemical  compounds  with  the  active  materials. 
It  remains  practically  constant  in  composition  and  density  through- 
out charge  and  discharge. 


58  RADIO    COMMUNICATION. 

The  voltage  while  charging  may  rise  to  1.8.  When  discharge 
begins,  the  voltage  drops  at  once  to  about  1.4,  then  falls  gradually, 
averaging  about  1.2  until  near  the  end.  The  discharge  should  not 
be  carried  beyond  the  point  at  which  the  open  circuit  voltage  is 
0.9.  During  the  charging  process  hydrogen  gas  is  given  off,  and 
since  this  forms  an  explosive  mixture  with  air,  an  open  flame  must 
never  be  brought  near  the  cells.  The  level  of  the  solution  must  be 
kept  above  the  tops  of  the  plates.  If  after  repeated  cycles  of  charge 
and  discharge  the  density  of  the  electrolyte  is  found  to  be  as  low  as 
1.16,  the  cells  should  be  completely  discharged,  and  the  old  electro- 
lyte should  be  replaced  by  new.  The  care  and  use  of  Edison  storage 
batteries  are  treated  in  great  detail  in  Radio  Pamphlet  No.  8,  and 
this  should  be  consulted. 

Comparison  of  the  Two  Types. — The  lead  cell  will  suffer  serious 
injury  if  not  charged  and  discharged  within  its  proper  limits  and  in 
a  regular  and  careful  manner.  The  Edison  cell,  however,  is  very 
rugged  and  will  maintain  its  efficiency  even  with  considerable  misuse. 
A  lead  cell  which  has  been  fully  charged  will  discharge  in  a  few 
weeks  if  left  standing  idle,  and  its  capacity  will  be  considerably 
decreased.  It  suffers  a  still  greater  loss  of  capacity  if  allowed  to 
stand  idle  while  discharged  or  in  a  partly  discharged  condition. 
The  Edison  cell,  on  the  other  hand,  will  retain  its  charge  over  a 
long  period  of  idleness,  and  it  may  be  allowed  to  stand  idle  for  an 
indefinite  time,  either  wholly  or  partly  discharged,  without  injury. 
A  complete  short  circuit  does  not  injure  an  Edison  cell,  but  will 
seriously  injure  a  lead  cell.  The  Edison  cell  can  be  charged  or 
discharged  at  rates  which  differ  greatly  from  the  normal,  without 
injury.  The  lead  cell,  however,  must  be  charged  or  discharged  at 
a  rate  very  close  to  its  normal  rate.  In  the  lead  cell  pure  water 
must  be  used  to  replace  evaporation  losses.  In  the  Edison  cell  any 
water  may  be  used  which  is  free  from  acids  and  sulphur. 

Some  Additional  Points. — In  charging,  it  is  necessary  to  allow 
about  2.5  volts  for  each  lead  cell,  and  about  1.75  volts  for  each 
Edison  cell.  If  the  line  voltage  is  not  sufficient  to  charge  the  entire 
set  of  cells  in  series,  they  may  be  divided  into  groups  and  these 
groups  may  be  placed  in  parallel. 

The  polarity  of  the  charging  line  may  be  tested  with  a  voltmeter, 
since  the  +  and  —  terminals  are  always  marked  on  the  instru- 
ment. If  a  voltmeter  is  not  at  hand,  a  pair  of  wires  from  the  line 
may  be  dipped  into  a  jar  of  slightly  acidulated  water.  Gas  bubbles 


RADIO   COMMUNICATION.  59 

will  form  about  one  wire  (the  negative)  much  faster  than  about  the 
other  (the  positive).  A  convenient  pole  testing  paper  may  be  made 
by  dipping  strips  of  paper  in  a  solution  of  potassium  iodide  in  water. 
If  the  wires  are  placed  on  such  a  strip  of  paper  a  few  centimeters 
apart,  and  gradually  brought  closer  together  (avoiding  direct  con- 
tact), a  brown  color  will  appear  about  the  +  pole.  Glycerin  may 
be  added  to  keep  the  solution  from  drying  out.  To  guard  against 
a  short  circuit  of  the  terminals  a  lamp  should  be  included  in  the 
circuit. 

22.  Internal  Resistance  in  Batteries. — It  has  been  stated  in 
Section  16  that  the  open  circuit  voltage  or  emf.  of  any  battery  is 
always  greater  than  the  terminal  voltage  measured  while  the  cell  is 
delivering  current.  The  relation  between  the  emf.  E,  the  ter- 
minal potential  difference  E',  and  the  internal  resistance  r  is 

given  by, 

E-E'=rI  (17) 

Moreover,  the  voltage  that  must  be  impressed  across  a  storage 
cell  to  charge  it  is  greater  than  the  emf.  of  the  cell,  by  the  voltage 
drop  within  the  cell  itself.  Representing  charging  voltage  by  E" ', 
and  with  the  other  symbols  having  the  same  meaning  as  above, 

E"-E=rI  (18) 

From  measurements  of  current  and  open  and  closed  circuit  volt- 
age, the  internal  resistance  of  the  battery  may  be  calculated.  The 
voltmeter  used  in  these  measurements  should  have  a  high  resistance, 
so  that  only  a  feeble  current  is  drawn  through  its  coil.  A  potenti- 
ometer is  ideal  for  this  measurement  (see  Sec.  26),  because  it  does 
not  draw  any  current  from  the  cell  at  the  instant  of  making  the 
measurement. 

It  is  important  to  understand  that  the  quantity  r,  which  has  been 
called  the  internal  resistance  of  a  battery,  is  not  a  constant,  but 
varies  with  the  current  drawn  from  the  cell.  In  some  cells  (e.  g., 
the  gravity  cell)  the  resistance  decreases  with  an  increase  of  current. 
In  others  (e.  g.,  the  dry  cell)  there  is  a  rapid  polarization  which 
tends  to  increase  with  the  current  output,  and  the  back  emf.  of 
polarization  opposes  the  emf.  of  the  cell  and  decreases  the  current 
flow.  The  effect  is  the  same  as  an  increase  in  resistance  of  the 
battery.  Thus  it  is  seen  that  although  the  factor  r  is  an  important 
one,  and  is  treated  as  a  resistance,  it  is  not  altogether  a  true  ohmic 
resistance.  A  better  name  for  it  is  the  apparent  or  effective 
resistance. 


60  RADIO    COMMUNICATION. 

E.  Electric  Circuits. 

23.  Current  Flow  Requires  a  Complete  Circuit. — In  order  to 
maintain  a  steady  flow  of  current,  there  must  be  a  continuous  con- 
ducting path.  This  path  is  called  the  "electric  circuit/'  and  it 
must  extend  out  from  the  generator  and  back  to  it  again.  The 
amount  of  current  which  flows  will  be  larger  as  the  resistance  of  the 
circuit  is  less.  If  some  part  of  the  circuit  is  made  of  very  high  re- 
sistance material,  the  current  which  is  maintained  is  relatively  small. 
The  complete  circuit  consists  of  two  parts,  (a)  the  external  part  of 
the  circuit,  which  connects  the  poles  of  the  battery  or  dynamo  out- 
side; and  (6)  the  internal  part  of  the  circuit,  which  is  made  up  of 
the  liquid  conductor  of  the  battery  or  the  wires  in  the  dynamo. 
When  the  wire  of  a  complete  circuit  is  cut  and  the  ends  separated,  the 
circuit  is  said  to  be  opened  or  broken.  If  the  ends  of  the  wire  are 
again  joined,  the  circuit  is  said  to  be  closed. 

Current  Value  Does  not  Vary  Along  the  Circuit. — The  beginning 
student  often  has  the  idea  that  a  current  may  start  out  from  a  source  at  a 
given  strength  and  then  in  some  way  become  used  up  or  dwindle  away 
as  it  goes  on  along  the  circuit.  This  is  entirely  a  wrong  conception 
and,  at  the  outset,  it  must  be  understood  that  in  simple  circuits  for 
steady  currents,  in  which  we  are  dealing  with  resistance  only,  the 
current  has  the  same  value  at  whatever  point  in  the  circuit  is  under 
consideration.  As  an  illustration  of  this,  consider  the  circuit  of 
Fig.  31,  made  up  of  a  battery  or  dynamo  G,  a  lamp  e,  and  a  resistor  E. 
If  the  circuit  is  cut  at  a,  6,  c,  or  at  any  other  point,  and  a  current- 
measuring  instrument  (an  ammeter)  inserted,  it  will  indicate  the 
same  value  of  current.  What  this  value  may  be  is  determined  of 
course  by  the  voltage  applied  and  the  total  resistance  in  the  circuit 
but  whatever  its  value,  it  is  constant  throughout  the  circuit.  This 
is  not  the  case  with  a.c.  circuits,  which  have  distributed  capacity. 
(See  Sec.  139.) 

The  same  idea  may  be  applied  to  a  circuit  such  as  that  shown  in 
Fig.  32.  The  total  current  /  divides  at  a  into  two  parts,  i\  and  i2. 
The  sum  of  these  components  is  exactly  equal  to  /.  In  other  words, 
whatever  current  flows  up  to  the  point  a,  flows  away  from  there. 
Also  the  currents  %  and  i2  unite  again  at  6  to  form  the  current  J, 
which  has  the  same  value  as  before. 

Another  important  law  is  that  the  sum  of  the  voltage  drops  in  every 
part  of  the  circuit,  including  the  generator,  is  equal  to  the  emf.  of 


RADIO   COMMUNICATION. 


61 


the  generator.  This  has  already  been  explained  in  connection  with 
Ohm's  law,  Section  16. 

24.  Series  and  Parallel  Connections. 

(a)  Resistances  in  Series. — If  several  resistors  are  connected  as 
shown  in  Fig.  33,  so  that  whatever  current  flows  through  one  of  them 
must  flow  through  all  the  others,  they  are  said  to  be  in  "series." 
The  single  equivalent  resistance  which  may  replace  the  entire  group 
without  changing  the  value  of  the  current,  is  equal  to  the  sum  of  the 
separate  resistances.  This  may  be  proved  as  follows.  The  voltages 


- 

A—  JWW  -  (WW>  -  fWWV-t 

I.   *    J         I.   E«   J         L  e»  J 


i.  fcl 

V* 
.b 


FIG. 


eS  in    Parallel 
FlQ.34 


across  /?,,  -R2,  R3,  etc.,  may  be  represented  by  E^  E2,  E3,  etc.    We 
may  then  write 

%±RJ 

E2=R2I 


Since  the  over-all  voltage  between  a  and  6  is  the  sum  of  the  volt- 
ages across  the  separate  parts  of  the  circuit,  we  may  write  for  the 
total  voltage  E, 

E=E1+E2+E3=R1I+R2I+RSI 
=I[Rl+R2+R3\ 
=IR 

where  R  replaces  the  sum  of  all  the  terms  in  the  bracket,  and  is  seen 
to  be  the  sum  of  the  separate  resistances. 


62  RADIO    COMMUNICATION. 

If  a  number  of  equal  resistances  are  connected  in  series,  we  may 
write  for  the  equivalent  resistance  of  the  group, 

R=nr  (19) 

where  n  is  the  number  and  r  is  the  resistance  of  each.  When  resist- 
ances are  connected  in  series,  it  must  be  remembered  that  the  current 
is  constant  and  the  total  voltage  is  subdivided  among  the  various  parts  of 
the  circuit. 

(b)  Resistances  in  Parallel.  —  If  several  resistances  are  connected 
as  shown  in  Fig.  34,  so  that  only  a  part  of  the  current  passes  through 
each  resistance,  they  are  said  to  be  connected  in  '•parallel"  or 
"  multiple."  The  voltage  E  between  points  a  and  b  is  the  same  over 
any  branch.  We  may  then  write,  from  equation  (11), 


Since  the  total  current  must  be  the  sum  of  the  three  branch  cur- 
rents, we  may  add  the  three  equations  and 


or 


From  equation  (9)  it  appears  that  the  voltage  divided  by  the 
current  gives  the  resistance,  hence  the  left-hand  member  of  equation 

(20)  is  the  reciprocal  of  the  equivalent  resistance,  or  -~- 
Hence 


Two  resistances  in  parallel  occur  so  often  in  practice,  that  it  is 
well  to  consider  this  case  further.  Solving  equation  (21)  for  R  when 
there  are  only  two  component  resistances  we  have, 

(22) 

Thus,  two  resistances  in  parallel  have  a  joint  or  equivalent  resistance, 
given  by  the  product  of  the  resistances  divided  by  their  sum. 


RADIO  COMMUNICATION. 


63 


When  there  are  a  large  number  of  single  resistances,  all  of  the  same 
value,  in  parallel,  it  can  be  shown  that  the  equivalent  resistance  of 
the  group  is  given  by 

R=^  (23) 

where  r  is  the  value  of  one  resistance,  and  n  is  the  number  of  them. 


When  resistances  are  connected  in  parallel  it  must  be  remembered  that  the 
voltage  across  ab,  Fig.  34,  is  constant,  and  the  total  current  is  subdi- 
vided among  the  several  branches.1 

1  Exercise  1. — A  current  of  42  amp.  flows  in  a  circuit,  Fig.  35,  and  divides  into  three 
parts  in  the  three  branches,  of  resistance  5  ohms,  10  ohms,  and  20  ohms,  respectively. 
Find  the  current  in  each  branch. 

Solution.— The  total  resistance  R  between  a  and  &  is  given  by 


10+20 
R=  j  ohms. 

The  RI  drop  between  a  and  6  is,  from  equation  (10),  E=~x  42  =  120  volts.    The 
several  currents  may  then  be  calculated  from  Ohm's  law, 

f 5=  ^=24  amp. 
o 

*io=~=12amp. 


120  =      =  6  amp. 

Exercise  2.— A  battery  of  internal  resistance  1  ohm  and  15  volts  emf.  is  sending  cur- 
rent through  a  circuit  with  resistances  as  shown  in  Fig.  36.  Find  (1)  the  total  current, 
(2)  the  RI  drops  across  resistances  1,  4,  and  5,  (3)  the  currents  through  1,  4,  and  5. 


64 


RADIO    COMMUNICATION. 


(c)  Batteries  in  Series  and  Parallel. — It  is  frequently  necessary, 
when  using  batteries,  to  increase  the  effect  which  a  single  cell  can 
produce.  This  is  done  by  connecting  the  batteries  in  any  one  cf 
three  ways: 

1.  In  series.     Here  the  +  side  of  one  cell  is  connected  to  the  - 
side  of  the  next  one,  and  so  on  for  all  the  cells.     (Fig.  37.) 

2.  In  parallel.     In  this  case  all  the  +  terminals  are  connected 
together  and  all  the  —  terminals  are  connected  together.     (Fig.  38.) 

3.  In  a  combination  of  series  and  parallel  groups.     Several  group 
of  cells  in  series  may  be  connected  in  parallel,  Fig.  39,  or  several 
groups  of  cells  in  parallel  may  be  connected  in  series.     (Fig.  40.) 


WH 


— \AAA/WW — 

Cells  ;„  5er.e5 


r~TT 

r  r  r 


C<=115    '"    Parallel 


Three  Series  Groups  in  Parallel 
FlQ.59 


Three  Parallel  Greu>i  in  Series 

Fiq.  4o 


The  proper  combination  to  use  in  any  given  case  is  dependent  upon 
circumstances,  but  in  general  a  series  arrangement  builds  up  voltage, 
hut  at  the  same  time  it  increases  the  internal  resistance,  while  a 
parallel  arrangement,  by  decreasing  the  internal  resistance,  permits 
greater  current  to  flow.  If  we  represent  the  number  of  cells  by  n, 
the  emf.  of  each  cell  by  E,  the  internal  resistance  of  one  cell  by  r, 
and  the  external  resistance  by  R,  we  may  write  Ohm's  law  for  each 
of  the  above  cases. 


RADIO   COMMUNICATION.  65 

For  series  arrangement, 


For  parallel  arrangement, 

/=7TZ  (25) 


For  n  cells  in  series  in  each  group,  and  m  such  groups  in  parallel, 


_ 

nr  (26) 

?M 

If  it  is  desired  to  build  up  a  large  current  through  R  with  a  given 
number  of  dry  cells,  especially  when  their  internal  resistance  has 
become  relatively  large  through  age,  a  series  arrangement  may 
actually  cause  the  internal  resistance  to  increase  faster  than  the 
voltage.  Hence,  adding  cells  in  series  would  result  in  a  decrease  of 
current.  The  best  use  of  a  given  number  of  cells  to  produce  a  stated 
current,  under  fixed  external  circuit  resistance,  can  only  be  deter- 
mined by  a*  careful  application  of  Ohm's  law  and  the  above  equa- 
tion, having  the  entire  circuit  in  mind.1 

i  Exercise.—  Assume  a  battery  of  two  dry  cells  in  series,  each  cell  having  an  emf.  of 
1.5  volts  and  an  internal  resistance  of  0.3  ohm.  Each  battery  then  has  an  emf.  of  3 
volts  and  an  internal  resistance  of  0.6  ohm.  Suppose  that  the  external  resistance  in 
the  circuit  is  0.2  ohm,  and  that  a  current  of  6  amp.  is  to  be  established. 

Solution.  —  If  we  try  one  battery,  Ohm's  law  gives 


This  is  not  enough  current,  so  we  will  try  two  batteries  in  series, 


The  current  is  still  too  small  and  it  is  seen  that  although  the  voltage  has  been 
doubled,  the  current  has  only  been  increased  by  about  14  per  cent.  Trying  three 
batteries  in  series, 


This  is  still  too  small  and  only  represents  an  increase  of  20  per  cent,  although  the 
voltage  was  increased  threefold.  We  will  now  try  an  arrangement  of  two  batteries 
in  parallel, 

'Tw*S 

97340° — 19 5 


RADIO    COMMUNICATION. 


In  general  the  largest  current  from  a  given  number  of  cells  will  be 
obtained  when  they  are  so  grouped  that  the  internal  resistance  of 
the  battery  is  equal  to  the  external  resistance  of  the  circuit.  Bat- 
teries will  be  connected  in  series  when  the  external  resistance  is 
large,  and  in  parallel  when  the  external  resistance  is  small.  In 
lighting  systems,  with  many  incandescent  lamps  in  parallel,  the 
lamp  resistance  is  large  compared  to  the  line  resistance,  and  very 
nearly  the  full  voltage  is  realized  at  the  lamp  socket. 

25.  Divided  Circuits.  The  Shunt  Law. — Electric  circuits  are 
frequently  arranged  so  that  the  total  current  is  subdivided,  and 
made  to  flow  through  two  or  more  branches  in  parallel.  As  shown 
in  Fig.  41  the  total  current  /divides  into  two  parts,  i\  and  i.2,  which 


FIG. 41 


nt  of  CorrenT  by  R>tenti'omet«r 
FK3.-43 


-— -o*— - 


Potent,  o  meter 

FlQ    47. 


flow  in  branches  r^  and  r2  respectively.  When  so  arranged,  either 
branch  is  called  a  shunt  (side  track  or  by  pass)  with  respect  to  the 
other.  The  voltage  between  points  a  and  6  is  of  course  the  same 
over  either  of  the  branches.  We  may  then  write, 

h-f  (a) 

E 


Dividing  (a)  by  (b)  we  have 


(27) 


RADIO   COMMUNICATION.  67 

The  currents  in  the  two  branches  are  inversely  proportional  to  the 
resistances  of  their  respective  paths.  This  relation  is  called  the 
"shunt  law."  In  other  words,  it  means  that  the  branch  of  lower 
resistance  carries  the  larger  current,  and  the  branch  of  higher  resis- 
tance carries  the  smaller  current. 

This  law  is  of  constant  application  in  electric  circuits.  Suppose 
that  the  only  ammeter  available  is  one  with  a  scale  range  of  0-5 
amp.,  and  suppose  that  a  current  of  50  amp.  has  to  be  measured. 
The  shunt  law  at  once  suggests  that  we  may  proceed  as  follows. 
With  50  amp.  flowing  in  the  main  circuit,  and  with  5  amp.  as  the 
safe  current  through  the  ammeter,  a  shunt  s  must  be  provided 
capable  of  carrying  the  rest  of  the  current  or  45  amp.  We  may  then 
write  from  equation  (27), 

JHs-f  (2'8> 

where  r  is  the  resistance  of  the  ammeter,  and  s  is  the  resistance  of 
the  shunt. 

Then  s=^r 

iJ 

Thus  to  carry  the  required  amount  of  current,  the  shunt  resistance 
must  be  one-ninth  of  that  of  the  ammeter.  In  general  it  can  be 
proved  that  if  /is  the  total  current,1 

»«=/r-4- 


S-\-T 

The  factor is  called  the  "multiplying  factor"  of  the  shunt, 

and  is  in  the  above  case  equal  to  10. 

26.  The  Potentiometer.2 — The  potentiometer  is  primarily  an 
arrangement  of  circuits  for  measuring  potential  difference  or  voltage. 
With  the  aid  of  certain  accessories  it  can  be  used  for  measuring  volt- 
ages over  all  ranges,  and  by  means  of  Ohm's  law  these  measurements 
can  be  applied  to  the  determination  of  a  wide  range  of  current  values. 
A  uniform  homogeneous  wire,  usually  a  meter  or  more  in  length 
(Fig.  42),  is  stretched  between  binding  posts  on  a  baseboard,  by  the 

1  For  proof  of  this  equation  see  Swoope,  Lessons  in  Practical  Electricity,  p.  146. 

2  The  word  "potentiometer"  is  used  here  in  its  original  sense,  meaning  an  arrange- 
ment of  circuits  for  measuring  potential  difference.    In  apparatus  catalogues  and  in 
textbooks  on  radio  circuits  the  word  is  often  inaccurately  used  in  the  sense  of  a 
voltage  divider.    (See  Sec.  15.) 


68  RADIO    COMMUNICATION. 

side  of  a  graduated  scale.  In  series  with  this  wire  is  a  constant 
source  of  current,  usually  a  storage  battery  WB  and  a  variable  re- 
sistor R.  From  equation  (10)  it  is  clear  that  by  properly  adjusting 
R  the  voltage  between  A  and  B  can  be  varied  through  wide  limits. 
Let  us  assume  that  (1)  the  end  A  is  connected  to  the  +  side  of  the 
battery  WB,  (2)  the  resistance  of  AB  is  uniform  from  end  to  end, 
and  (3)  the  current  through  AB  is  constant  and  of  such  a  value  that 
the  RI  drop  along  the  wire  is  about  2  volts.  If  a  standard  cell,  of 
voltage  E  (about  1.0183),  has  its  +  pole  connected  to  the  point  A, 
a  certain  point  c1  can  be  found,  such  that  when  contact  is  made  at 
this  point,  the  galvanometer  g  (see  Sec.  50)  will  show  no  deflec- 
tion. The  absence  of  deflection  on  the  galvanometer  means  that 
the  7?/drop  in  the  wire  AB  up  to  the  point  q  is  just  equal,  and  opposed 
to  the  voltage  of  the  standard  cell.  The  distance  Ac^  may  be  rep- 
resented by  d\.  Xow  let  some  other  cell  E/,  whose  voltage  is  to  be 
tested,  be  put  in  place  of  the  standard  cell  E.  If  the  voltage  of  this 
cell  does  not  exceed  the  RI  drop  in  AB,  another  point  c.2  can  be 
found,  for  which  there  is  no  current  through  the  galvanometer.  The 
distance  Ac2  may  be  called  d2,  and  the  RI  drop  over  this  length  of 
wire  is  just  equal  and  opposed  to  the  voltage  of  the  cell  E/  to  be  tested. 
Since  the  RI  drops  along  the  wire  are  directly  proportional  to  the 
lengths,  we  may  write 


and 

'  (30) 


This  simple  form  of  the  apparatus  is  only  capable  of  measuring  a 
voltage  not  much  greater  than  that  of  the  standard  cell.  If  very 
much  higher  voltages  are  to  be  measured,  the  high  voltage  is  put 
across  the  terminals  of  a  voltage  divider  (Sec.  15),  and  some  defi- 
nite fraction  of  it  is  then  measured  against  the  standard  cell,  as 
described  above. 

Also,  any  range  of  current  can  be  measured  by  means  of  the  poten- 
tiometer. The  current  to  be  measured  is  passed  through  a  standard 
resistance  ab  of  known  value  R,  Fig.  43.  This  is  so  chosen  that  the 
.RJdrop  across  it  lies  within  the  voltage  range  of  the  potentiometer. 
The  determination  of  current  then  consists  in  measuring  the  voltage 
across  ab  in  terms  of  the  standard  cell,  and  calculating  the  current 
bv  Ohm's  law. 


RADIO   COMMUNICATION.  69 

27.  The  Wheatstone  Bridge. — This  is  a  simple  circuit  for  meas- 
uring an  unknown  resistance  in  terms  of  a  known  resistance.  The 
method  depends  upon  the  fact  that  in  a  branched  circuit,  Fig.  44, 
the  voltage  drop  from  a  to  c  must  be  the  same  over  the  path  abc  as 
it  is  over  the  path  adc.  It  then  follows  that  for  any  point  b  which 
may  be  chosen  on  the  upper  circuit  abc,  there  must  be  some  point 
d  on  the  lower  branch,  such  that  there  will  be  no  difference  of  po- 
tential between  it  and  the  point  b.  The  point  d  can  be  found  by 
connecting  one  terminal  of  a  galvanometer  at  b  and  moving  the  con- 
tact point  connected  to  the  other  terminal  along  the  lower  wire 
until  there  is  no  deflection.  This  means  that  there  is  no  current 
flowing,  and  hence  no  potential  difference  between  b  and  d.  When 
the  points  b  and  d  have  been  located  in  this  way,  it  can  be  shown  l 
that  there  is  a  simple  definite  relation  between  the  resistances  of 


^^VW^-T-^WWN 

\  .  T.  / 

^A/VW-^vVVW 

ThncifAs  of  the  WSeAtstone   Bridge 


the  four  arms  of  the  circuit.  (See  Fig.  45.)  If  three  of  these  resist- 
ances are  known,  the  fourth,  r.(,  can  be  readily  calculated  from  the 
equation 


*~\  (31) 

In  practice  the  branch  adc  may  be  made  from  a  long,  uniform  and 
homogeneous  wire,  in  which  case  it  is  not  necessary  to  know  the 
resistance  values.  If  the  portion  abc  is  such  a  wire,  the  ratio  of  the 
lengths  It  and  12  of  the  segments  will  be  the  same  as  the  ratio  of  the 
resistances.  The  equation  (31)  may  then  be  written 


For  proof  of  this  equation  see  Timbie,  Elements  of  Electricity,  p.  107. 


70  RADIO    COMMUNICATION. 

28.  Heat  and  Power  Losses. — In  Section  7  it  was  shown  that 
when  current  flows  through  a  resistance,  heat  is  generated  in  it.  It 
is  important  to  understand  that  this  effect  does  not  refer  to  heating 
the  resistor  to  a  definite  temperature,  but  rather  it  has  to  do  with  the 
generation  of  heat  at  a  definite  rate.  This  rate  may  be  expressed  in 
joules  per  second,  calories  per  second,  watts,  or  horsepower.  When 
the  rate  of  supply  of  heat  due  to  the  electric  current  is  just  equal  to 
the  rate  of  loss  of  heat  by  conduction  or  radiation,  then  the  tempera- 
ture becomes  constant.  The  final  temperature  of  any  resistance  coil 
through  which  current  is  passing  depends  upon  its  surroundings.  If 
it  is  open  to  the  air,  radiation  is  more  free.  In  coils  which  are  in- 
closed, the  temperature  may  rise  rapidly  and  unless  care  is  taken, 
the  insulation  may  be  softened  or  even  burned. 

When  the  heat  is  dissipated  at  as  fast  a  rate  as  it  is  produced,  so 
that  the  temperature  of  the  resistor  remains  constant,  the  resistance 
becomes  constant. 

Equation  (2)  is  W=  JH=RPt  (2) 

Since  from  Ohm's  law,  I—E/R  we  may  write 


E 
Again  substituting  R=j> 

we  have  W=JH=~=EIt  (33) 

These  three  equations  will  give  the  energy  in  joules  when  am- 
peres, ohms,  volts,  and  seconds  are  used. 

Power  is  the  time  rate  of  change  of  energy.  If  the  three  equations 
above  are  divided  by  the  time  t,  we  have  the  corresponding  three 
equations  for  power. 

P==RP  (34) 


(35) 
=EI  (36) 

Exercise  1.  What  power  is  required  to  operate  1000  incandescent  lamps,  each  of 
which  requires  \  amp.  and  110  volts? 
First  solution.  —  From  equation  (36),  each  lamp  requires 

iX  110=  55  watts. 
For  1000  lamps  — 

'  1000X  55=  55,000  watts 

=  55  kw. 


RADIO   COMMUNICATION. 


71 


Since 


746  watts=  1  horsepower, 

55,000    „ 
-^--73.7  h.p. 


Second  solution.—  The  resistance  of  each  lamp  is  given  by 


Using  equation  (34) 
For  1000  lamps— 


*----  220  ohms. 

P=  220X  1=  55  watts  for  1  lamp. 
P=  1000X55=  55  kw. 


Exercise  2.  An  instrument  has  1210  ohms  resistance  in  its  coils,  and  a  voltage 
of  110  volts  is  impressed.    Calculate  the  rate  of  dissipation  (watt-loss)  in  the  coils. 

F.  Capacitance. 

29.  Dielectric  Current. — So  far,  only  steady  currents  and  their 
flow  in  conductors  have  been  considered.     In  a  perfect  insulating 


FIG.4& 


Electric  Strain  or  Displacement 


\\\\\\\\\\H\\W\ 


Construct!  "on    <jf 
Condenser 

Fia.46 


material,  current  can  flow  only  momentarily.  If  an  electromotive 
force  is  applied  between  two  points  of  an  insulator,  a  momentary 
flow  of  current  takes  place  which  soon  ceases.  The  current  flow  is 
very  different  from  that  in  a  conductor.  If  a  very  sensitive  indicator 
of  current  g,  Fig.  46,  is  connected  into  the  circuit,  it  shows  a  sudden 
deflection  when  the  key  is  closed.  This  deflection  soon  drops  to 
zero.  The  momentary  flow  of  electricity  is  due  to  the  production  of 


72  RADIO    COMMUNICATION. 

a  sort  of  electric  strain  or  "displacement"'  of  electricity.  This  is 
resisted  by  a  sort  of  elastic  reaction  of  the  insulator  that  may  be 
called  electric  stress.  On  account  of  this  reaction  of  the  electric 
stress,  the  electric  strain  due  to  a  steady  applied  emf.  reaches  a 
steady  value,  and  the  current  becomes  zero.  When  the  electric 
strain  is  subsequently  allowed  to  diminish,  a  current  again  exists  in 
the  opposite  direction.  A  current  of  this  kind,  called  a  "displace- 
ment current,"  exists  only  when  the  electric  strain  or  displacement 
is  changing.  When  considering  the  existence  of  electric  strain  or 
displacement  in  an  insulating  material,  the  material  is  called  a 
"dielectric,"  and  the  displacement  current  is  sometimes  called  a 
"dielectric  current." 

We  do  not  think  of  this  electric  displacement  as  being  due  to  the 
actual  passage  of  matter,  on  which  the  charge  is  carried  from  one 
plate  to  the  other,  nor  even  from  one  molecule  to  another  within  the 
substance.  It  is  rather  as  if,  in  each  molecule,  a  positive  charge  is 
moved  to  one  end  and  a  negative  charge  to  the  other.  Then  with  all 
the  positive  charges  pointing  in  one  direction,  the  effect  is  that  a  cer- 
tain change  has  been  transmitted  clear  across  the  dielectric.  An 
illustration  may  aid  in  making  this  idea  clearer.  In  a  dense  crowd  of 
people,  a  sudden  push  or  shove  on  one  person  will  be  sent  through 
from  person  to  person.  Energy  is  transmitted,  and  yet  no  single 
person  has  passed  all  the  way  across. 

When  a  dielectric  is  in  the  electrically  strained  condition,  it 
possesses  potential  energy  in  the  "electrostatic ''  form.  (For  a  brief 
discussion  of  energy,  see  C.  74,  p.  9.) 

30.  Condensers. — Displacement  is  produced  in  a  dielectric  by 
placing  the  dielectric  between  metal  plates  and  connecting  a  battery 
or  other  source  of  emf.  to  these  plates.  Such  an  arrangement  con- 
sisting of  metal  plates  separated  by  a  non-conducting  material  is 
called  a  condenser.  Thus  in  Fig.  47,  A  and  B  are  the  metal  plates 
of  the  condenser.  The  dotted  lines  indicate  the  directions  of  the 
electric  strain  or  displacement.  The  plate  from  which  the  displace- 
ment takes  place  is  called  the  positive  or  +  plate  of  the  condenser. 
Conversely,  the  other  plate  is  called  the  negative  or  —  plate.  The 
dielectric  may  be  air  or  other  gas,  or  any  solid  or  liquid  that  is  not  a 
conductor.  When  the  battery  is  connected  to  the  condenser,  a 
displacement  current  begins  to  flow,  continuing  until  the  electric 
displacement  reaches  its  final  or  steady  value.  The  displacement 
produced  depends  upon  (a)  the  voltage  applied  to  the  condenser 


RADIO   COMMUNICATION.  ,    75 

C^ 

and  (6)  the  kind  of  dielectric.     A  continuous  or  direct 
flow  only  in  conductors.     An  alternating  current,  in    , 
direction  periodically  changes  sign,  can  flow  also  in  condt 
the  form  of  a  dielectric  current.     (See  Sec.  58.)     In  this  ca.         .<? 
electric  strain  or  displacement  reverses  its  direction  with  every 
reversal  of  the  current.     The  existence  of  the  electric  strain  or 
displacement  in  the  dielectric  is  equivalent  to  the  presence  of  a 
certain  quantity  or  charge  of  electricity. 

For  a  given  condenser,  its  charge  Q  is  found  to  be  directly  propor- 
tional to  the  applied  voltage  E.  This  relation  may  be  written 

Q=CE  (37) 

where  C  is  a  constant.  For  any  given  condenser  the  value  of  this 
constant  is  seen  to  be  the  ratio  of  the  charge  to  the  voltage,  or 

C=|  (38) 

This  constant  is  called  the  '"capacitance"  of  the  condenser.  The 
units  used  for  capacitance  are  the  "microfarad"  and  the  "micromi- 
crofarad,"  abbreviated  as  "mfd."  and  "micro-mfd."  (See  defini- 
tion in  Appendix  2,  p.  350.) 

The  capacitance  changes  when  different  dielectric  materials  are 
used.  If  the  plate  area  is  increased,  the  capacitance  increases  in 
direct  ratio,  and  as  the  plates  are  brought  closer  together,  the  capaci- 
tance increases.  (Formulas  for  calculating  the  capacitance  of  con- 
densers are  given  in  C.  74,  p.  235.) 

Charging  of  Condensers. — During  the  brief  time  in   which  the 

charge  is  accumulating  in  a  condenser,  the  voltage  -^  due  to  this 
charge  is  increasing.  This  voltage  tends  to  oppose  the  applied  or 

charging  voltage.     When  -^  has  become  equal  to  E,  the   charging 
u 

process  comes  to  an  end.  It  will  be  noticed  that  equation  (37)  does 
not  contain  a  time  factor;  therefore  the  same  amount  of  charge  is 
stored  in  a  condenser  whether  it  is  built  up  slowly  or  quickly.  How- 
ever, the  rate  of  building  up  the  charge  depends  upon  the  value  of 
the  capacitance  and  resistance  of  the  circuit.  The  larger  the  product 
of  the  factors  C  and  R  the  greater  is  the  time  required  to  arrive  at  any 
given  fraction  of  the  applied  voltage;  this  product  CR  is  called  the 
time  constant  of  the  circuit. 


72^""  RADIO    COMMUNICATION. 

^ 

31.  Dielectric  Properties.  —  A  simple  experiment  will  show  that 
the  charge  accumulated  in  a  condenser,  for  a  given  voltage  and  dis- 
tance apart  of  the  plates,  depends  upon  the  kind  of  dielectric  mate- 
rial. A  pair  of  plates  with  dry  air  between  them  is  charged  by  a 
certain  emf  .  ,  and  the  quantity  or  amount  of  charge  is  measured  by 
some  suitable  means.  If  now  a  slab  of  paraffin  be  inserted  between 
the  plates,  it  is  found  that  for  the  same  voltage  the  charge  is  in- 
creased. Denoting  the  capacitance  with  air  by  Ca  and  the  capaci- 
tance with  paraffin  by  Cp,  we  may  write 


where  Kis  a  constant.  By  simply  changing  the  dielectric  material, 
and  without  changing  the  geometric  arrangement  of  the  plates,  we 
find  that  the  capacitance  has  been  increased  .  Air  is  commonly  used 
as  the  standard  of  comparison,  and  the  factor  Kis  called  the  "  dielec- 
tric constant"1  of  the  material.  The  dielectric  constant  of  any  sub- 
stance may  then  be  defined  as  the  ratio  of  the  capacitance  of  a  condenser 
using  this  substance  as  the  dielectric,  to  the  capacitance  of  the  same  con- 
denser with  air  as  the  dielectric.  This  ratio  is  seen  to  be  the  factor  by 
which  the  capacitance  of  an  air  condenser  must  be  multiplied  in 
order  to  find  the  capacitance  of  the  same  condenser  when  the  new 
substance  is  used.  Some  values  are  given  below. 


Substances. 

Values  of 
dielectric 
constant. 

Paper  dry 

1  5 

Paper  (treated  as  used  in  cables)  

4 

Paraffin    .  .  . 

2  to  3  3 

Ebonite 

2  to  3  2 

Petroleum  

2  1 

Transformer  oil   . 

2  5 

Mica 

4  to  8 

Glass      

4  to  10 

Water       

81 

A  wide  variation  is  seen  in  the  values  given  for  some  substances, 
inasmuch  as  the  properties  of  such  materials  differ  greatly  with  the 
rapidity  or  slowness  with  which  the  charge  is  applied  or  withdrawn. 
Quite  different  values  of  K  will  be  found,  if  the  measurements  are 
made  with  a  rapidly  reversed  voltage  and  with  a  slowly  applied 

1  Sometimes  called  also  "inductivity"  or  "specific  inductive  capacitance." 


RADIO   COMMUNICATION.  75 

voltage  from  a  battery.  For  accurate  values,  the  conditions  of  use 
must  be  very  precisely  stated. 

Dielectric  materials  are  not  perfect  insulators,  but  do  have  a  very 
small  electric  conductivity.  A  condenser  will  permit  a  very  small 
current  to  flow  through  it  continuously  when  a  voltage  is  applied 
to  its  terminals,  and  it  will  discharge  itself  slowly,  if  allowed  to  stand 
with  its  terminals  disconnected.  This  is  called  the  "  leakage"  of  the 
condenser.  Materials  differ  greatly  in  this  respect.  A  pair  of  plates 
with  dry  air  as  dielectric  will  retain  the  charge  almost  indefinitely 
after  the  voltage  is  cut  off,  while  in  some  paper  condensers  the  charge 
disappears  by  leakage  in  a  few  minutes. 

If  an  emf.  gives  a  condenser  a  certain  charge  when  applied  for  a 
short  time,  and  a  greater  charge  when  applied  for  a  longer  time,  the 
dielectric  is  said  to  possess  "absorption."  There  is  a  gradual  pene- 
tration of  the  electric  strain  into  the  dielectric,  which  requires  time. 
When  the  terminals  of  a  charged  condenser  are  connected  by  a  con- 
ductor, a  current  flows  and  the  condenser  discharges.  The  charge 
which  flows  out  instantaneously  upon  discharge  is  called  the  "  free 
charge."  With  some  dielectrics,  if  the  terminals  are  connected  a 
second  time,  another  and  smaller  discharge  occurs,  and  this  may  be 
repeated  several  times.  This  so-called  residual  charge  is  due  to  the 
absorbed  charge,  and  indicates  a  slow  recovery  of  the  dielectric  from 
the  electric  stress.  In  condensers  made  with  oil  or  well  selected 
mica  for  the  dielectric,  absorption  is  small.  It  is  larger  with  glass, 
and  very  troublesome  with  bakelite  and  similar  materials.  After 
charging  such  a  condenser  with  a  high  voltage,  the  absorbed  charge 
continues  to  be  given  up  for  a  long  time.  Absorption  is  accompanied 
by  the  production  of  heat  in  the  dielectric.  This  represents  a  loss 
of  energy. 

The  ratio  of  the  free  charge  of  a  condenser  to  the  voltage  across  its 
terminals  is  called  the  "geometric  capacitance."  Any  measure- 
ments of  capacitance  which  make  use  of  a  prolonged  time  of  charging, 
yield  values  larger  than  the  geometric  capacitance.  Measurements 
made  with  high-frequency  alternating  currents  give  values  which 
approach  closely  to  the  geometric  capacitance. 

Summary. — An  elastic  body  is  distorted  or  strained  by  placing  it 
under  the  action  of  a  stress;  and  the  effect  produced  is  measured  in 
terms  of  the  flexibility  of  the  material.  A  dielectric  substance  is 
strained  electrically  by  placing  it  under  the  action  of  an  emf.,  and 
the  effect  produced  is  measured  in  terms  of  the  capacitance  of  the 


76  RADIO    COMMUNICATION. 

condenser.  It  is  of  interest  to  note  that  the  capacitance  of  an  electric 
condenser  is  directly  analogous  to  flexibility,  or  stretchability  of 
an  elastic  body. 

32.  Types  of  Condensers. — In  order  fr>  increase  the  capacitance 
of  a  condenser,  we  may — 

1.  Increase  the  area  of  the  plates. 

2.  Diminish  the  distance  between  the  plates. 

3.  Use  a  substance  of  larger  dielectric  constant. 

In  general,  condensers  are  classified  in  two  groups,  as  they  may 
be  designed  respectively,  for  (a)  low  voltage — less  than  500  volts, 
or  (6)  high  voltage — several  thousand  volts.  Increasing  the  plate 
area  tends  to  increase  the  bulk  and  weight  of  the  condenser.  Bring- 
ing the  plates  very  close  together  makes  necessary  the  use  of  a  sub- 
stance of  high  dielectric  strength  if  the  voltage  is  high.  For  low  volt- 
age service,  where  large  capacitance  is  essential,  the  condenser  plates 
are  made  of  tin  foil  with  thin  sheets  of  mica  or  paraffined  paper  between 
them.  The  sheets  are  piled  up  as  shown  in  Fig.  48,  p.  71.  The 
dielectric  layers  are  represented  by  aa,  and  the  two  sets  of  conducting 
plates  by  bb,  and  cc,  respectively.  These  are  pressed  into  a  com- 
pact form  and  held  in  place  by  a  clamp,  flowing  the  entire  set  of 
plates  with  melted  paraffin  or  wax.  If  the  condenser  must  withstand 
a  very  high  voltage,  the  plates  will  be  more  widely  separated  and 
usually  air  or  oil  is  used  as  the  dielectric.  If  it  is  desired  to  have  the 
capacitance  of  the  condenser  variable  instead  of  fixed,  the  construc- 
tion usually  takes  the  form  shown  in  Fig.  49.  Two  sets  of  inter- 
leaved plates  are  insulated  from  each  other,  and  one  set  is  mounted 
so  that  it  can  be  rotated  with  respect  to  the  other.  Such  a  condenser 
can  be  calibrated  so  that  the  capacitance  corresponding  to  any 
angular  setting  of  the  rotating  part  is  known.  Condensers  used  in 
radio  circuits  are  represented  by  certain  symbols.  These  may  be 
found  in  Appendix  3,  page  354. 

It  is  not  always  necessary  that  the  conducting  plates  in  the 
condenser  should  be  sheets  of  metal.  The  earth  is  a  conductor 
and  frequently  replaces  one  plate  in  the  system.  A  wire  stretched 
on  a  pole  line  forms  one  plate  of  a  condenser,  and  the  other  plate 
may  be  the  neighboring  return  wire  of  the  circuit,  or  it  may  be 
the  earth  itself.  Several  wires  in  a  connected  group  will  have 
more  capacitance  with  respect  to  the  earth  than  a  single  wire. 
Such  a  condenser  is  the  radio  antenna.  (Fig.  50.)  The  conduct- 
ing core  of  a  submarine  cable  forms  one  plate  of  a  condenser,  the 
insulating  material  is  the  dielectric  and  the  sea  water  is  the  other 


RADIO   COMMUNICATION. 


77 


plate.  Similarly  in  a  telephone  cable,  paper  is  the  dielectric,  and 
any  single  conductor  of  the  cable  may  be  regarded  as  one  plate, 
the  other  plate  being  the  adjacent  wire  of  the  pair,  or  the  lead 
sheath  of  the  cable  itself.  The  great  length  of  such  wires  and 
cables  givrs  them  large  surface  and  hence  large  capacitance.  A 
mile  of  standard  sea  cable  may  have  a  capacitance  of  about  J  nifcl. 
A  mile  of  standard  telephone  cable  should  not  have  capacitance 
of  more  than  about  0.08  mfd.  The  capacitance  of  a  pair  of  No. 
8  copper  wires,  1000  ft.  in  length  and  32  in.  apart  is  about 
0.0032  mfd.  Two  square  plates  10  cm.  on  a  side,  separated 


flO.51 


by    1    mm.    of    dry    air    have    a    capacitance    of    approximately 
100  micro-mfd.     (For  such  calculations  see  C.  74,  p.  235.) 

33.  Electric  Field  Intensity. — Consider  the  air  condenser  shown 
in  Fig.  51,  having  an  emf.  E  applied  across  its  terminals.  The 
emf.  is  the  cause  of  the  electric  strain  or  displacement  which  is  in 
the  direction  shown  by  the  dotted  lines.  The  emf.  between  the 
plates  of  the  condenser  is  equivalent  to  a  force  acting  at  every 
point  of  the  dielectric,  which  would  cause  a  body  having  a  charge 
of  electricity  to  move.  This  is  called  the  electric  field  intensity 
and  is  denned  as  the  force  per  unit  charge  of  electricity.  The 
space  in  which  this  field  intensity  acts  is  called  an  electric  field. 


78 


RADIO    COMMUNICATION. 


The  value  of  the  electric  field  intensity  at  any  point  inside  the 
condenser  shown  in  Fig.  51  is  the  ratio  of  the  emf.  across  the 
condenser  to  the  distance  between  the  plates.  Electric  field 
intensity  £,  is  thus  given  by 

&=f  (39) 

where  E  is  the  emf.  between  two  points  in  the  dielectric  a  distance 
d  apart.  £,  is  commonly  expressed  in  volts  per  centimeter.  It 
is  a  quantity  of  importance  in  connection  with  electric  waves. 

The  electric  field  in  the  condenser  of  Fig.  51  is  the  same  every- 
where in  direction  and  in  value.  This  is  called  a  uniform  field. 
There  are  many  other  kinds  of  fields.  The  electric  field  about 
two  small  unlike  charges  is  shown  in  Fig.  52.  Another  example 


Fl<3   5Z                                     FlO.53^> 
/ 

-t!^"~"*<w 

\ 

""\  ^ 

X\     \    \ 

?\\  '; 
Vi\  i 

1   !  !    !    ! 

Electric  Field    between  Two                                           |     |    f  f 

LUctnc  Field  About  Verti'ea 
Wire 

is  given  by  two  bodies,  one  of  which  is  a  long  vertical  wire,  and 
the  other  is  a  conductor  extended  in  a  horizontal  direction.  These 
amount  to  two  conductors  separated  by  a  dielectric  (air),  thus 
fulfilling  the  definition  of  a  condenser.  Suppose  the  lower  body 
is  the  earth  itself,  which  is  a  conductor.  The  field  about  the 
system  will  be  represented  by  Fig.  53.  This  represents  the  form 
of  condenser  and  electric  field  in  the  case  of  the  radio  antenna. 

34.  Energy  Stored  in  a  Condenser. — The  electric  strain  in  the 
dielectric  of  a  charged  condenser  represents  a  store  of  energy.  The 
amount  of  energy  stored  in  this  way  is  found  as  follows.  The  work 
done  in  placing  a  charge  in  a  condenser  is  the  product  of  the  charge 
by  the  voltage  between  the  plates.  Suppose  a  condenser  is  charged 
by  applying  to  it  an  emf.  which  begins  at  a  zero  value  and  rises 
to  E  volts.  The  increase  in  voltage  is  uniform  and  hence  the 


RADIO   COMMUNICATION.  79 

average  voltage  is  \  E.  The  energy  stored  in  the  condenser  is  the 
product  of  this  by  the  charge,  thus 

W=\  QE  (40) 

Since  Q=CE,  from  equation  (37),  we  may  write 

W=\  CE2  (41) 

The  work  is  expressed  in  joules  when  the  capacitance  is  in  farads 
and  the  emf .  is  in  volts.  A  capacitance  of  0.001  mfd.  charged  with 
an  emf.  of  20,000  volts  has  a  store  of  energy  given  by 

W=$  ^j^X20,0002=0.2  joules 

From  equation  (41)  it  appears  that  time  does  not  enter  into  the 
energy  equation.  For  a  given  condenser  charged  to  a  given  voltage 
it  requires  the  same  total  amount  of  energy,  whether  the  charge 
is  acquired  slowly  or  rapidly. 

The  total  amount  of  work  done  in  charging  a  condenser  divided 
by  the  time,  gives  the  power  expended.  This  may  be  written, 

?=l™ 

or 

P=i  CE2  N  (42) 

where  T  is  the  time  in  seconds  required  to  complete  the  charge, 
and  N  is  the  number  of  charges  completed  in  one  second  of  time. 
If  the  condenser  in  the  above  problem  is  charged  by  a  generator 
giving  an  alternating  emf.  with  a  frequency  of  500  cycles  per 
second,  the  power  becomes 

p=i  OE2JV=0.200X1000=200  watts. 

It  will  be  noted  that  the  condenser  is  charged  and  discharged 
twice  in  every  complete  cycle  of  the  a.c,  generator;  also  that  Eis 
the  maximum  emf. 

35.  Condensers  in  Series  and  in  Parallel. — Just  as  it  is  sometimes 
found  convenient  to  combine  resistances  into  series  or  parallel 
groups,  so  it  is  often  desirable  to  combine  condensers.  The  capaci- 
tance of  the  group,  however,  is  not  calculated  the  same  way  as  in 
the  case  of  resistances. 

Condensers  in  Parallel. — Fig.  54  shows  three  condensers  con- 
nected in  parallel.  The  condensers  are  all  under  the  same  im- 
pressed emf.,  and  they  accumulate  charges  proportional  to  their 


80 


RADIO    COMMUNICATION. 


respective  capacitances.  It  has  been  stated  in  Section  30  that 
capacitance  is  proportional  to  plate  area.  Connecting  condensers 
in  parallel  is  equivalent  simply  to  increasing  the  plate  area.  If  C\ 
C2,  C3,  etc.,  represent,  respectively,  the  capacitances  of  the  conden- 
sers of  the  group,  and  if  C  represents  the  equivalent  capacitance  of 
the  entire  group,  we  may  then  write 


C-- 


(4.3) 


Parallel  connection  of  condensers  always  gives  a  larger  capacitance 
than  that  of  any  single  member  of  the  group. 

Condensers  in  Series. — If  several  condensers  are  connected  as  shown 
in  Fig.  55  they  are  said  to  be  connected  in  series.  In  finding  the 
equivalent  capacitance  of  such  a  group,  it  must  be  kept  in  mind  that 


FlQ.54 


¥ 


Corvder 


Parallel 


FiQ.  55 


the  same  charge  is  given  to  each  condenser,  and  that  the  total  voltage 
E  is  subdivided  among  the  condensers  in  direct  ratio  to  their  capaci- 
tances. Using  symbols  as  above  we  may  then  write 


or  since  in  general  E= 


Whence 


Q    Q   ,Q  ,Q   , 

0=0+0+0  + 

1    1  ,  1  ,  1  , 
c=c+c+c+ 


(44) 


Series  connection  of  condensers  always  gives  a  smaller  capacitance 
than  that  of  any  single  member  of  the  group.  (See  problems  below.) 

1.  A  condenser  has  a  capacitance  of  0.014  mfd.,  and  it  is  charged  with  an  emf. 
of  30,000  volts. 

Find  (a)  the  charge  in  the  condenser,  (6)  the  energy  stored,  (c)  the  power  expended 
when  charged  by  a  500-cycle  ax:,  generator. 


RADIO   COMMUNICATION. 


81 


2.  A  condenser  is  built  up  of  15  parallel  and  circular  plates.    Each  plate  is  20  cm.  in 
diameter  and  the  separation  is  1  mm.    Petroleum  is  used  as  a  dielectric.    Calculate 
the  capacitance.    (See  C.  74,  p.  235.) 

3.  Three  condensers  have  capacitances  of  0.02,  0.20  and  0.05  mfd.,  respectively. 
Find  the  equivalent  capacitance,  (a)  when  they  are  all  in  series;  (6)  when  they  are 
all  in  parallel. 

G.  Magnetism. 

36.  Natural  Magnets. — One  of  the  forms  in  which  iron  is  found  in 
the  earth  is  the  black  oxide  of  iron  (chemical  formula  Fe3O4),  called 
magnetite  or  magnetic  iron  ore.     A  piece  of  this  substance  is  called 
a  "natural  magnet,"  and  it  has  two  very  remarkable  properties  as 
follows: 

(a)  If  a  piece  of  it  is  dipped  into  iron  filings  the  filings  will  adhere 
to  it. 

(6)  If  a  piece  of  it  is  suspended  by  a  silk  thread,  or  by  a  thin 
untwisted  cord,  it  will  set  itself  with  its  longer  axis  very  nearly  in  a 
north  and  south  direction. 

37.  Bar  Magnets. — A  small  rod  of  iron  or  steel  which  is  brought 
near  to  a  piece  of  magnetite,  or  which  is  rubbed  on  it  in  a  certain 


F1Q.56* 


by  Hie  EleefH 

Current 


FIQ.57 


way,  shows  the  same  properties,  and  is  said  to  be  "magnetized." 
If  the  rod  or  bar  is  made  of  rather  hard  steel,  the  effect  persists  after 
the  iron  ore  has  been  taken  away,  and  the  magnetized  rod  is  then 
called  a  "permanent  magnet,"  or  simply  a  bar  magnet.  These 
permanent  magnets  may  be  made  in  the  form  of  straight  bars  of  round 
or  square  section,  usually  with  the  length  rather  large  as  compared 
to  the  diameter.  They  are  also  often  bent  into  various  shapes,  a 
common  form  being  the  horseshoe  or  U-shaped  magnet. 
97340° — 19 6 


82 


RADIO    COMMUNICATION. 


Magnets  may  also  be  made  by  passing  an  electric  current  through 
a  coil  of  wire  which  surrounds  the  rod.  (See  Fig.  56.)  If  the  rod  is 
made  of  soft  iron,  it  is  only  magnetized  as  long  as  the  current  flows. 
It  is  then  called  a  temporary  magnet  or  an  " electromagnet."  Ex- 
amples of  electromagnets  are  seen  in  induction  coil  and  buzzer  cores, 
in  telegraph  sounders  and  relays  and  in  telephone  receivers.  Elec- 
tromagnets are  very  useful  because  the  magnetism  is  so  easily  con- 
trolled by  variations  in  the  current  strength.  If  the  bars  are  of 
hardened  steel,  the  magnetism  due  to  the  current  remains  after  the 
current  ceases  and  a  permanent  magnet  is  the  result. 

A  slender  magnetized  steel  rod  mounted  carefully  on  a  pivot 
(Fig.  57)  will  turn  very  nearly  into  the  north  and  south  position,  and 
is  called  a  ''compass  needle."  It  is  used  by  sailors  and  surveyors 
for  determining  directions.  The  end  which  points  north  is  called 


Lints 


of  force  around  a  bar  ma£r,«' 
ens  of  exf>lorir\^-  needle 

„  FlO.59 


Simple    theory  of* 

Earthb  magnetic  field 


field  Aboyt  A"  b*r 
by    iron  filings 


the  north-pointing  or  simply  the  "north  pole."     The  other  end  is 
called  the  south  pole. 

38.  The  Magnetic  Field. — If  a  compass  needle  is  placed  at  various 
positions  near  a  large  bar  magnet,  it  changes  its  direction  as  shown 
in  Fig.  58.  This  shows  that  in  the  space  all  around  the  magnet 
there  are  forces  which  act  on  magnetic  poles.  If  iron  filings  are 


RADIO   COMMUNICATION.  83 

sprinkled  on  a  level  sheet  of  paper  which  lies  over  the  magnet,  the 
filings  arrange  themselves  as  shown  in  Fig.  59.  Each  little  par- 
ticle of  iron  acts  like  the  compass  needle  and  points  in  a  definite 
direction  at  a  given  position.  These  direction  lines,  called  "mag- 
netic lines  of  force,"  all  appear  to  center  in  two  points  near  the  ends 
of  the  bar  magnet.  These  points  are  called  the  "  poles  "  of  the  mag- 
net. Two  magnetic  poles  are  said  to  be  alike  when  they  both 
attract  or  both  repel  the  same  pole.  If  one  attracts  and  the  other 
repels  the  same  pole,  they  are  said  to  be  unlike.  Like  poles  repel 
each  other  and  unlike  poles  attract  each  other.  It  is  then  easy  to  de- 
termine which  is  the  north  and  which  is  the  south  pole  of  a  bar 
magnet  by  means  of  the  direction  in  which  the  north  pole  of  a 
compass  needle  points. 

The  region  all  about  a  magnet,  in  which  these  forces  on  the  poles 
of  magnetic  needles  may  be  detected,  is  called  the  "magnetic 
field."  The  intensity  of  a  magnetic  field  may  be  defined  in  terms 
of  the  force  which  acts  on  a  given  magnetic  pole,  or  it  may  be  de- 
fined in  another  way,  as  described  in  a  following  paragraph.  The 
direction  of  a  magnetic  field  is  defined  as  the  direction  in  which 
the  north  pole  points. 

The  earth  has  a  magnetic  field  about  it  which  is  represented  by 
Fig.  60.  This  field  is  similar  to  that  which  exists  about  a  bar 
magnet  placed  within  the  earth  with  its  ends  at  the  North  and 
South  Poles  of  the  earth. 

39.  Magnetic  Flux  and  Flux  Density. — The  arrangement  of  the 
iron  filings  in  Fig.  59  shows  that  there  is  a  greater  effect  at  some 
points  than  at  others.  It  also  suggests  that  the  lines  of  force  may 
be  thought  of  as  similar  to  stream  lines  in  a  moving  fluid.  From 
this  point  of  view  there  is  said  to  be  a  magnetic  flux  through  the 
space  occupied  by  the  magnetic  field.  This  is  represented  by 
lines  drawn  closer  together  where  the  field  is  strong  and  farther 
apart  where  the  field  is  weak.  The  magnetic  field  must  not  be 
thought  of  as  made  up  of  filaments,  like  a  skein  of  yarn,  because  it 
really  is  continuous.  However,  electrical  engineers  represent  a 
magnetic  flux  by  drawing  one  line  through  the  field  for  each  unit  of 
the  flux.  The  number  of  such  lines  through  each  square  centimeter 
of  the  field  perpendicular  to  the  lines  is  the  "magnetic  induction " 
or  "flux  density."  The  unit  of  flux  density  exists  in  a  magnetic 
field  when  the  unit  of  magnetic  flux  is  distributed  over  a  square 
centimeter  of  area,  taken  perpendicular  to  the  direction  of  the  flux. 


84 


RADIO    COMMUX ICATIOX . 


40.  The  Magnetic  Field  about  a  Current. — It  has  already  been 
pointed  out  in  Section  3  that  there  is  a  magnetic  field  about  a  wire 
in  which  a  current  is  flowing.  Experiments  with  the  compass  show 
that  this  magnetic  field  has  lines  of  force  in  the  form  of  concentric 
circles  about  the  wire.  These  circles  lie  in  planes  at  right  angles 
to  the  axis  of  the  wire.  If  the  wire  is  grasped  by  the  right  hand 
with  the  thumb  pointing  in  the  direction  of  the  current,  the  fingers 
will  show  the  direction  of  the  magnetic  field  (Fig.  10).  This  field 
extends  to  an  indefinite  distance  from  ,the  conductor,  but  for  points 
farther  from  the  wire  the  effect  becomes  more  feeble,  and  the  more 
S3iisitive  must  be  the  apparatus  for  detecting  it.  If  the  current 


P  i  a .  G>I 

-Solenoid 


Field   of    OolenwW 


stops,  the  magnetic  field,  together  with  its  effects,  disappears.  When 
current  is  started  through  the  wire,  we  may  think  of  the  magnetic 
field  as  coming  into  being  and  sweeping  outward  from  the  axis  as  a 
center.  This  disappearing  and  rebuilding  of  the  magnetic  field 
as  the  current  decreases  and  increases  will  be  made  use  of  in  Sec- 
tion 46,  in  explaining  some  important  principles  which  apply  in 
radio  circuits. 

41.  The  Solenoid  and  the  Electromagnet. — If  the  wire  which 
carries  a  current  is  bent  into  a  circle,  the  magnetic  field  is  of  the  form 
shown  in  Fig.  61.  At  the  center  of  the  circle  the  field  is  uniform 
only  for  a  very  small  area.  If  many  turns  are  wound  close  together 


RADIO   COMMUNICATION.  85 

in  what  may  be  called  a  bunched  winding,  the  intensity  of  the 
magnetic  field  is  increased  in  direct  proportion  to  the  number  of 
turns.  When  the  wire  is  wound  closely  with  many  turns,  side  by 
side  along  the  surface  of  a  cylinder,  the  coil  is  called  a  "solenoid," 
Fig.  62.  In  this  case,  the  magnetic  field  is  nearly  uniform  for  a  con- 
siderable distance  near  the  center  of  the  coil,  and  the  solenoid  has 
the  properties  of  a  bar  magnet.  This  is  seen  by  comparing  the 
magnetic  fields  of  Figs.  63  and  59.  The  intensity  of  the  field  and 
the  magnetic  flux  density  within  the  solenoid,  depend  entirely  upon 
the  strength  of  the  current  and  the  number  of  turns  of  wire  per  centi- 
meter. The  same  magnetizing  effect  can  be  secured  with  many 
turns  and  a  weak  current,  or  with  a  few  turns  and  a  strong  current, 
provided  only  that  the  product  of  wire  turns  times  amperes  of  cur- 
rent is  the  same  in  each  case.  This  product  is  called  the  "ampere- 
turns."  In  round  numbers  the  magnetizing  field  strength,  repre- 
sented by  the  symbol  H,  is  given  by 

5  /ampere-turns\ 
~4\       length      ) 

If  /  is    the    current  in    amperes  the    accurate    formula  may    be 

written  l 

4       NT 

ff-ro'T-  (46> 

42.  Magnetic  Induction  and  Permeability. — If  the  space  within 
the  solenoid  is  filled  with  iron,  the  magnetic  flux  lines  are  very 
greatly  increased.  This  is  due  to  a  property  of  iron  called  magnetic 
' '  permeability. ' '  To  say  that  iron  is  more  permeable  than  air  means 
that  the  magnetism  is  stronger  when  iron  is  present  than  it  would 
be  if  the  space  were  filled  with  air  alone.2  Permeability  varies 
according  to  the  quality  of  the  iron,  from  a  few  units  to  a  few  thou- 
sand. For  example,  to  say  that  the  permeability  of  a  certain  sample 
of  iron  is  1000  means  that  the  magnetic  flux  through  1  cm.  of 
cross  section  of  the  iron  is  1000  times  as  great  as  the  flux  through 

1  For  proof  of  this  formula  see  C.  74,  p.  15. 

2  Time  is  required  for  the  magnetization  to  travel  inward  from  the  surface  to  the 
axis  of  the  iron  core.    Hence,  if  the  current  is  rapidly  reversed  in  direction,  the  mag- 
netic wave  started  by  one-half  cycle  does  not  have  time  to  travel  inward  appreciably 
before  the  reversed  half  cycle  recalls  it  and  starts  a  wave  of  opposite  sign.     As  a  con- 
sequence the  magnetism  is  confined  to  the  outer  layers  of  the  iron  core.    For  this 
reason  iron  is  not  as  effective  in  increasing  the  number  of  flux  lines  in  high  frequency 
circuits,  as  it  is  with  steady  currents  or  low  frequency  currents. 


86  RADIO    COMMUNICATION. 

the  same  area  before  the  iron  was  present.  The  total  magnetic  flux 
through  an  iron  core  within  a  magnetizing  coil,  divided  by  the  area 
of  cross  section,  gives  the  "magnetic  induction,"  which  is  repre- 
sented by  the  symbol  B.  We  may  denote  total  flux  through  the 
iron  by  0i?  then 

4^=BA  (47) 

where  A  is  the  area  of  cross  section  of  the  iron  core.  If  the  intensity 
of  the  magnetizing  field  within  a  solenoid  is  denoted  by  H,  then  the 
total  magnetic  flux  through  the  solenoid  is  given  by 

<t>&=HA  (48) 

where  A  is  the  area  of  cross  section  and  </>a  is  the  total  flux  through 
the  air  core.  The  permeability  is  denned  as  the  ratio  of  B  to  H. 

It  is  important  that  the  student  should  remember  that  the  mag- 
netic induction  depends  upon  (a)  the  number  of  ampere-turns  and 
(6)  the  property  of  iron  called  permeability.  The  number  of  ampere- 
turns  is  under  the  control  of  the  operator.  The  permeability  de- 
pends upon  the  quality  of  the  iron  itself. 

If  the  current  in  the  windings  is  reversed,  the  direction  of  the 
magnetic  field  is  also  reversed.  The  student  should  learn  at  least 
one  rule  for  remembering  the  relation  between  the  direction  of  the 
current  and  the  direction  of  the  magnetic  flux.  Two  such  memory 
helps  are  here  given. 

(a)  Look  along  the  direction  of  the  lines  of  magnetic  flux  through 
the  solenoid,  and  the  current  is  in  a  clockwise  direction. 

(6)  Grasp  the  solenoid  with  the  right  hand,  the  fingers  pointing 
along  the  wires  in  the  direction  of  the  current.  The  thumb  then 
points  in  the  direction  of  the  magnetic  flux  inside  of  the  solenoid.1 

43.  The  Force  on  a  Conductor  Carrying  Current  in  a  Magnetic 
Field. — If  two  different  magnetic  fields  are  brought  together  in  the 
same  space,  with  their  directions  parallel,  a  force  is  always  de- 
veloped. If  the  lines  of  magnetic  flux  are  in  the  same  direction, 
the  two  fields  mutually  repel  one  another,  and  if  the  flux  lines  are 
in  opposite  directions  the  two  fields  will  be  drawn  together.  When 
a  current  flows  in  a  wire  which  is  at  right  angles  to  a  magnetic 
field,  a  force  will  act  on  the  wire.  A  rule  which  will  help  the 
student  to  remember  the  direction  of  the  motion,  together  with 

1  Apply  each  of  the  above  rules  to  Fig.  62.  Also  wind  an  experimental  solenoid 
with  a  few  feet  of  wire,  connect  it  to  a  dry  cell  and  mark  in  some  way  the  direction 
of  current  through  the  windings.  Test  its  polarity  with  a  compass,  remembering 
that  like  poles  repel  and  unlike  poles  attract. 


RADIO   COMMUNICATION.  87 

the  directions  of  current  and  field,  is  the  so-called  "left-hand 
rule."  Extend  the  forefinger  of  the  left  hand  in  the  direction  of 
the  magnetic  field,  and  hold  the  middle  finger  at  right  angles  to 
it  in  the  direction  of  the  current.  The  extended  thumb,  held  at 
right  angles  to  both  the  other  directions,  indicates  the  direction 
of  the  motion.  Note  that  this  rule  calls  for  the  use  of  the  left 
hand.  Compare  this  with  the  right  hand  rule  of  Section  45. 

When  the  wire  which  carries  the  current  is  at  right  angles  to  the 
direction  of  the  magnetic  field,  the  pushing  force  on  the  wire  is  equal 
to  the  product  of  the  current,  the  intensity  of  the  magnetic  field,  and 
the  length  of  wire  which  lies  in  the  magnetic  field. 

If  the  wire  makes  some  other  angle  with  the  direction  of  the  mag- 
netic field,  the  direction  of  the  force  is  still  the  same  as  for  the  right 
angle  position,  and  the  value  of  the  force  is  smaller.  In  the  single 
instance  that  the  direction  of  the  current  coincides  with  the  direction 
of  the  magnetic  field  the  force  is  zero. 

This  push  on  a  single  wire  is  in  most  cases  small,  but  by  arranging 
many  wires  in  a  very  intense  magnetic  field,  very  large  forces  may 
be  obtained.  The  powerful  turning  effect  of  an  electric  motor 
depends  upon  these  principles.  (See  Sec.  96.) 

H.  Inductance. 

44.  The  Linking  of  Circuits  with  Lines  of  Magnetic  Flux. — There 
is  always  a  magnetic  field  about  an  electric  current.  The  lines  of 
magnetic  flux  are  closed  curves  and  the  electric  circuit  is  also  closed. 
The  lines  of  magnetic  flux  are  then  thought  of  as  always  interlinked 
with  the  wire  turns  of  the  circuit.  (See  Fig.  64.)  The  number  of  flux 
lines  through  a  coil  will  depend  upon  the  current,  and  any  change  in 
the  current  will  change  the  number  of  linkings.  If  there  are  two 
turns  of  wire  the  circuit  will  link  twice  with  the  same  magnetic  flux, 
and  so,  for  any  number  of  turns,  the  number  of  linkings  increases 
with  the  number  of  turns.  Let  </>  represent  the  number  of  magnetic 
flux  lines,  N  the  number  of  linkings  and  n  the  number  of  wire  turns. 
Then  it  is  seen  that  the  number  of  linkings  is  always  given  by 

N=n  0  (49) 

A  change  in  N  may  be  brought  about  by  (a)  a  change  in  <£,  due  to 

a  change  in  the  current,  or  (6)  a  change  in  the  number  of  wire  turns. 

Again  the  loop  of  wire,  Fig.  65,  not  now  connected  to  any  battery, 


88 


RADIO    COMMUNICATION. 


may  be  placed  near  a  bar  magnet,  or  a  solenoid  which  has  current 
flowing  in  it.  Some  of  the  flux  lines  will  pass  through  the  loop. 
The  number  of  these  flux  lines  is  represented  by  <f>  as  before,  and 
every  turn  of  wire  will  link  with  the  flux  lines.  Then  the  number 
of  linkings  is  given  by 

N=n  0  (50) 

which  is  the  same  expression  as  in  the  other  case. 

The  number  of  flux  lines  may  be  changed  by  changing  the  number 
of  wire  turns,  or  by  changing  the  number  of  flux  lines  through  the 
loop.  The  latter  may  be  done  by  rotating  the  loop,  or  by  moving 


Fl<3 


Lines  of  fo 


Lfnes  of  force  of  -solenoid   '  I  inK^ii.  witK  circuit  A6 

rQ- 


'       ,  v^»  ^      '  >      *» 

/  MAl^>n«^  fKrVst- 4rftcr  coil^of  wirax^  induces  emf; 


it  with  respect  to  the  magnet.  If  a  solenoid  is  used,  the  change  can 
be  made  by  variations  in  the  current  through  its  coils. 

45.  Induced  Electromotive  Force. — Whenever  there  is  any  change 
in  the  number  of  linkings  between  the  magnetic  flux  lines  and  the 
wire  turns,  there  is  always  an  emf.  induced  in  the  circuit.  If  the 
circuit  is  closed,  a  current  will  flow.  This  is  called  an  induced  cur- 
rent. Some  of  the  ways  in  which  this  is  accomplished  are  de- 
scribed in  the  following  paragraphs. 

1.  A  bar  magnet  is  pushed  into  a  closed  coil  of  wire,  Fig.  66. 
During  the  time  the  magnet  is  moving,  there  will  be  indications  on 
the  galvanometer  g  that  current  is  flowing.  When  the  magnet  is 


RADIO   COMMUNICATION.  89 

drawn  back,  away  from  the  coil,  a  current  is  induced  in  the  opposite 
direction.  The  direction  of  this  induced  current  will  always  be 
such  as  to  oppose  the  change  to  which  it  is  due.  That  is,  if  the 
magnet  is  approaching  the  coil,  the  current  will  flow  in  AB  so  that 
A  is  a  north  pole,  and  hence  the  magnet  will  be  repelled.  If  the 
key  Tc  is  open  the  induced  current  cannot  flow.  If  it  is  closed  an 
induced  current  does  flow,  and  sets  up  a  magnetic  field  about  the 
coil.  It  can  be  shown  that  more  work  is  required  to  move  the 
magnet  with  respect  to  the  coil  when  the  key  is  closed,  than  when 
it  is  open.  These  facts  are  expressed  in  the  law  of  Lenz,  which 
states  that  whenever  an  induced  current  arises,  by  reason  of  some  change 
in  Unkings,  the  magnetic  field  about  the  induced  current  is  in  such  a 
direction  as  to  oppose  the  change.  A  helpful,  mechanical  illustra- 
tion of  Lenz's  law  is  seen  in  the  effort  necessary  to  move  a  stationary 
body.  Owing  to  the  mass  of  the  body,  a  force  is  necessary  to  start  it, 
and  if  one  tries  to  move  it  suddenly,  he  will  experience  a  consider- 
able reacting  force.  This  reacting  force  will  be  greater  the  more 
sudden  the  change  in  the  motion  of  the  body.  Similarly  in  the 
electric  circuit,  the  induced  emf.  will  be  greater  the  more  sudden 
the  change  in  the  number  of  linkings. 

2.  The  same  effects  as  those  described  in  (1)  may  be  secured  if  the 
bar  magnet  is  replaced  by  a  solenoid  carrying  current. 

3.  The  effects  may  also  be  produced  by  two  solenoids  fixed  in  the 
position  shown  in  Fig.  67.     If  a  current  is  started  in  one  of  them, 
A,  there  will  be  a  current  induced  in  the  other,  which  will  continue 
to  flow  as  long  as  the  current  in  A  is  increasing.     If  the  current  in 
A  becomes  steady,  there  is  no  current  induced  in  B.     If  the  current 
in  A  falls  off,  the  induced  current  in  B  is  reversed  in  direction.     In 
all  cases  it  must  be  remembered  that  the  magnetic  field  about  the 
induced  current  tends  to  oppose  tho  change  that  is  causing  the 
induced  current. 

4.  A  further  example  of  induced  currents  is  found  in  the  case  of 
two  straight  wires,  Fig.  68,  close  together.     If  the  electric  current 
stops  (Fig.  69),  starts,  or  varies  in  one  of  them  in  any  way,  there  are 
corresponding  induced  currents  in  the  other.     This  case  of  parallel 
straight  wires  is  seen  in  certain  telephone  lines  where  cross  talk 
occurs,  or  where  there  is  interference  from  a.c.  power  lines.     Al- 
though we  think  of  the  straight  and  parallel  portions  of  the  circuit, 
we  must  not  overlook  the  fact  that  these  are  only  portions  of  com- 
pletely closed  circuits. 


90 


RADIO    COMMUNICATION. 


The  magnitude  of  the  induced  emf.  in  all  of  the  above  cases  depends 
upon  the  time  rate  of  change  of  the  number  of  Unkings.  This  may  be 
expressed  by  the  equation 


where  t  is  the  time  in  seconds  in  which  the  change  n<t>  takes  place. 
This  is  the  basic  principle  of  dynamo-electric  machinery. 

46.  Self  Inductance.  —  With    a  single    circuit    carrying    current, 
as  shown  in  Fig.  64,  the  magnetic  flux  <f>  which  threads  through 


I 


FIQ.  &6 

When*  ournent  is  st«*rtod  or  atoned  in  Current  starting,  in  A   induces 

circuit  A. an  errff.  IS  induced  in  circuit  &,  current  in   C> 


FlC3  TO 


Current"  at 
our  rant    in 


At   induces 


iTa     A  And   &    h< 
inductance 


the  circuit  (and  hence  the  number  of  linkings  N)  is  directly  pro- 
portional to  the  current  strength.     This  fact  may  be  expressed  by 

the  formula 

N=LI  (52) 

where  £  is  called  the  "self  inductance,"  or  simply  the  "inductance" 
of  the  circuit. 

The  value  of  L  depends  upon  the  number  of  wire  turns,  upon  the 
shape  and  size  and  upon  the  permeability  of  the  medium  about  the 
circuit.  For  air  the  permeability  is  1.  The  inductance  does  not 
depend  upon  the  current  which  is  flowing,  except  when  iron  is 


RADIO   COMMUNICATION.  91 

present.  By  coiling  up  a  piece  of  wire  in  many  turns  and  intro- 
ducing it  into  the  circuit,  the  inductance  of  the  circuit  may  b« 
greatly  increased.  In  that  case  the  inductance  is  said  to  be  con- 
centrated. It  must  not  be  overlooked  that  the  entire  circuit  has 
inductance.  This  may  be  distributed  more  or  less  uniformly 
throughout  the  circuit. 

If  a  piece  of  wire  is  connected  to  one  terminal  of  a  dry  cell,  and 
tapped  on  the  other  terminal,  a  very  slight  spark  may  be  seen  in  a 
darkened  room.  If  a  coil  of  many  turns  of  wire  is  included  in  series 
with  this  cell,  the  same  process  of  tapping  will  show  brilliant  sparks, 
particularly  if  the  coil  has  an  iron  core.  The  explanation  of  this 
lies  in  the  fact  that  the  cell  voltage  of  about  1.5  is  too  feeble  to  cause 
much  of  a  spark.  However,  when  the  large  inductance  is  included 
in  the  circuit,  there  is  a  large  number  of  linkings  between  wire 
turns  and  flux  lines.  If  these  flux  lines  collapse  suddenly,  as  they 
do  when  the  circuit  is  broken,  there  will  be  a  large  change  in  the 
number  of  linkings  taking  place  in  a  very  small  interval  of  time. 
From  equation  (51),  this  means  that  a  large  voltage  will  be  set  up. 
This  principle  is  made  use  of  in  ignition  apparatus  and  spark  coils 
of  various  types.  According  to  Lenz's  law,  the  induced  emf.  will 
be  in  such  a  direction  as  to  oppose  the  change  which  causes  it.  In 
this  case,  when  the  circuit  is  broken,  the  change  is  from  some  value 
of  current  /to  zero.  Therefore  the  induced  emf.  will  be  in  the  same 
direction  as  the  original  current,  and  will  try  to  keep  the  current 
flowing.  On  the  other  hand,  when  a  battery  is  being  connected  to 
an  inductive  circuit  by  means  of  a  switch,  the  rising  current  will 
establish  a  set  of  magnetic  flux  lines  which  will,  as  they  grow, 
induce  an  emf.  which  tends  to  keep  the  current  from  rising. 

47.  Mutual  Inductance. — Consider  a  circuit  AA,  Fig.  70,  with  a 
current  J  flowing  through  it.  The  magnetic  flux  through  A  is 
directly  proportional  to  /,  and  that  part  of  the  total  flux  which 
interlinks  with  a  near-by  coil  B  is  also  proportional  to  /.  This  means 
that  the  total  number  of  interlinkings  N,  between  flux  lines  that 
arise  in  the  A  circuit,  and  wire  turns  of  the  B  circuit,  is  proportional 
to  the  current  Jin  the  circuit  A.  This  fact  may  be  represented  by 
the  equation 

N=MI  (53) 

where  M  is  the  constant  of  proportionality.  This  factor  M  is  called 
the  "mutual  inductance"  of  the  two  circuits.  When  currents  are 


92  RADIO    COMMUNICATION. 

started,  stopped  or  varied  in  coil  A,  the  mutual  inductance  shows 
itself  by  an  emf.  induced  in  coil  B.  The  induced  emf.  may  be 
calculated  by 

E=M^  (54) 

where  I/  is  the  amount  by  which  the  current  in  the  A  circuit  varies 
in  the  time  t. 

In  radio  circuits  the  mutual  inductance  is  often  used  to  transfer 
power  from  one  circuit  to  another  when  there  is  no  conducting  path 
between  them. 

48.  Energy  Relations  in  Inductive  Circuits. — In  mechanics  it  is 
well  known  that  a  piece  of  matter  cannot  set  itself  in  motion  and 
that  energy  must  be  supplied  from  outside.  So  in  the  electric 
circuit,  a  current  cannot  set  itself  in  motion,  and  energy  must  be 
supplied  by  some  form  of  generator  (source  of  emf.).  It  has  already 
been  explained  how  a  magnetic  field  arises  about  electric  circuits. 
When  this  field  collapses  or  disappears,  the  energy  stored  in  the 
field  is  returned  to  the  circuit.  It  can  be  shown  that  the  energy 
thus  associated  with  a  magnetic  field  is  given  by  the  equation 

W=$LI2  (55) 

where  I'  is  the  value  of  the  current  and  L  is  the  self  inductance. 
The  student  who  is  familiar  with  the  laws  of  mechanics  will  note 
that  this  equation  is  quite  similar  to  that  for  kinetic  energy  of  a 
moving  body 

Kinetic  energy =%ms2 

where  in  is  the  mass  of  the  body  and  s  is  its  speed. 

Illustration  of  Inductance. — When  a  nail  is  forced  into  a  piece  of 
wood,  the  mere  weight  of  the  hammer  as  it  rests  on  the  head  of  the 
nail  will  produce  but  little  effect.  However,  by  raising  the  hammer 
and  letting  it  acquire  considerable  speed,  the  kinetic  energy  stored 
is  large,  and  when  the  motion  of  the  hammer  is  stopped  this  energy 
is  used  in  forcing  the  nail  into  the  wood.  In  the  electric  circuit  a 
cell  with  its  small  emf.  can  cause  only  a  feeble  spark.  By  including 
a  piece  of  wire  with  many  turns  in  the  circuit,  however,  energy  is 
stored  as  shown  in  equation  (55).  A  small  current  will  enable  a 
large  amount  of  energy  to  be  stored  in  the  magnetic  field,  if  L  is 
large.  Then  when  the  circuit  is  broken  and  the  field  collapses,  this 
large  amount  of  energy  is  released  suddenly,  and  a  hot  spark  of 
considerable  length  is  the  result. 


RADIO   COMMUNICATION.  93 

The  close  relations  between  capacitance,  inductance  and  resist- 
ance will  be  more  fully  discussed  in  Chapter  4. 

I.  Alternating  Current. 

49.  Reactance. — A  steady  current  in  a  circuit  meets  no  other 
hindrance  than  the  resistance  of  the  circuit.     If  the  current  changes, 
this  is  no  longer  true.     If  the  circuit  has  inductance,  the  current 
is  opposed  by  the  emf.  induced  by  the  variation  of  the  current. 
(See  Sec.  46.)     If  a  condenser  is  present,  this  is  constantly  charging 
or  discharging  as  the  current  changes,  and  it  exerts  a  controlling 
influence  on  the  passage  of  the  current.     If  both  inductance  and 
capacitance  are  included  in  the  circuit,  they  tend  to  offset  each 
other  in  their  effects,  but  usually  one  or  the  other  exerts  a  pre- 
dominating influence,  with  the  result  that  there  is  added  to  the 
resistance  an  extra  opposition  to  the  current,  which  is  known  as 
the  "reactance." 

The  more  rapid  the  changes  of  the  current,  the  greater  the  induced 
emf.  in  a  circuit  and  consequently  the  greater  the  inductive  re- 
actance. On  the  contrary,  the  reactance  of  a  condenser  is  less, 
the  more  rapidly  the  current  varies,  as  can  be  understood  when  we 
reflect  that  the  greater  the  number  of  charges  and  discharges  of  the 
condenser  performed  each  second,  the  greater  the  total  quantity 
of  electricity  which  flows  around  the  circuit  in  that  interval,  that  is, 
the  greater  the  current.  In  general,  the  reactance  of  a  radio  circuit 
is  very  much  greater  than  the  resistance. 

To  calculate  the  current  in  a  radio  circuit,  then,  it  is  necessary 
.to  know  how  to  calculate  the  reactance  and  how  to  combine  it  with 
the  resistance,  in  order  to  determine  the  total  hindrance  or  "im- 
pedance" to  the  current.  Since  the  reactance,  however,  depends 
upon  the  way  in  which  the  current  is  varying,  it  is  evident  that  this 
must  be  definitely  specified  in  each  case.  The  problem  cannot  be 
solved  for  all  imaginable  kinds  of  variation  of  the  current.  Radio 
currents,  however,  belong  to  the  general  class  of  alternating  currents, 
and  for  these,  the  theory  is  rather  simple.  In  the  following  sections 
is  given  a  brief  treatment,  not  of  general  alternating  current 
theory,  but  merely  of  those  alternating  current  principles  which 
are  essential  to  an  understanding  of  the  actions  in  radio  circuits. 

50.  Nature  of  an  Alternating  Current. — An  alternating  current  is 
one  in  which  electricity  flows  around  the  circuit,  first  in  one  direction 
and  then  in  the  opposite  direction,  the  maximum  value  of  the 


94 


RADIO    COMMUNICATION. 


current  in  one  direction  being  equal  to  the  maximum  value  in  the 
other.  All  the  changes  of  current  occur  over  and  over  again  at 
perfectly  regular  intervals. 

Sine  Wave. — To  get  an  insight  into  the  nature  of  such  a  current, 
suppose  a  case  where  the  alternations  occur  so  slowly  that  we  may 
follow  the  changes  of  current  with  an  ammeter.  In  the  table  below 
are  given  values  of  the  so-called  "sine  wave  current''  at  successive 
equal  intervals  of  time.  The  maximum  value  is  taken  as  10  amp. 


Time 

(sec). 

Current 
(amp). 

Time 

(sec). 

Current 
(amp). 

Time 
(sec). 

Current 
(amp). 

0 

0 

13 

-  2.59 

25 

2.59 

1 

2.59 

14 

-  5.00 

26 

5.00 

2 

5.00 

15 

-  7.07 

27 

7.07 

3 

7.07 

16 

-  8.66 

28 

8.66 

4 

8.66 

17 

-  9.66 

29 

9.66 

5 

9.66 

18 

-10.00 

30 

10.00 

6 

10.00 

19 

-  9.66 

31 

9.66 

7 

9.66 

20 

-  8.66 

32 

8.66 

8 

8.66 

21 

-  7.07 

33 

7.07 

9 

7.07 

22 

-  5.00 

34 

5.00 

10 

5.00 

23 

-  2.59 

35 

2.59 

11 

2.59 

24 

0 

36 

0 

12 

0 

The  ammeter  in  such  a  case  would  creep  slowly  up  to  a  maximum 
indication  of  10  amp. ,  return  gradually  to  zero,  reverse  its  direction 
and  build  up  to  a  value  of  10  amp.  in  the  opposite  direction,  then 
decrease  to  zero  again,  build  up  again  in  the  original  direction,  and 
so  on.  It  is,  of  course,  to  be  understood  that  the  current  assumes  in 
turn  all  possible  values  between  zero  and  the  maximum  value  (10 
amp.  in  this  case),  and  that  the  current  has  the  same  value  through- 
out the  circuit  at  every  moment.  The  current  in  this  case,  as  well 
as  that  of  a  steady  current,  may  be  regarded  as  like  the  flow  of  an 
incompressible  fluid.  The  emf.  is,  however,  to  be  regarded  here  as 
a  variable  electric  pressure,  which  acts  first  in  one  direction  and 
then  in  the  other. 

The  values  of  current  in  the  preceding  table  are  plotted  in  Fig. 
71  as  ordinates  (vertically),  and  the  corresponding  lengths  of  time 
elapsed  since  the  start,  as  abscissas  (horizontally),  and  a  smooth 
curve  drawn  through  the  points  enables  one  to  determine  what  is 
the  value  of  the  current  for  any  moment  lying  between  any  two  of 
those  which  are  included  in  the  table.  It  is  to  be  noted  that  the 
changes  of  current  repeat  themselves.  Thus  in  the  table  the  current 
is  the  same  at  1  sec.  and  25  sec.  after  the  start;  at  7  sec.  and  31  sec., 


RADIO  COMMUNICATION. 


95 


etc.  The  interval  of  24  seconds  in  this  example  is  the  "period" 
of  this  alternating  current.  The  current  passes  through  a  complete 
" cycle"  of  changes  in  one  period. 

A  current  like  that  just  treated  is  the  same  as  that  which  would 
be  produced  in  a  circuit  attached  to  a  coil  revolving  very  slowly 
in  a  uniform  magnetic  field.  (See  Chap.  3,  Sec.  62.)  The  motion 
has  been  assumed  slow  in  order  that  the  changes  can  be  followed 
with  ordinary  direct  current  instruments.  In  order  to  represent 
the  current  developed  by  an  ordinary  low  frequency  alternating 
current  generator,  we  must,  however,  imagine  the  coil  to  revolve 
more  than  a  thousand  times  more  rapidly.  Thus  the  usual  a.c. 
lighting  circuits  carry  currents  whose  period  is  only  about  •$•$  second. 
The  current  passes  through  60  complete  cycles  each  second,  that  is, 


its  "frequency"  is  60  cycles  per  second.  Ordinary  alternating- 
current  generators  cannot  use  magnetic  fields  which  are  entirely 
uniform,  so  that  the  current  obtained  never  passes  through  its 
changes  in  exactly  the  same  way  as  the  ideal  sine  current  pictured 
in  Fig.  71.  The  difference  is,  however,  usually  so  small  in  well- 
designed  machines  that  it  does  not  need  to  be  taken  into  account. 

The  frequency  of  radio  currents  is  enormously  greater  than  the 
usual  low  frequency  alternating  currents.  In  order  that  Fig.  71 
may  properly  represent  a  radio  current,  we  must  suppose  a  whole 
cycle  to  be  completed  in,  say,  Toow<n7  to  •nmnnr  second. 

51.  Average  and  Effective  Values  of  Alternating  Current.— In  just 
the  same  way  as  we  have  analyzed  alternating  current  by  imagining 
it  to  change  slowly,  it  is  possible  to  get  an  insight  into  complicated 
movements,  like  the  throwing  of  a  ball  or  the  galloping  of  a  horse, 
by  running  a  motion-picture  film  of  the  action  so  slowly  that  the 
separate  pictures  on  the  film  can  be  examined  one  at  a  time. 


96  RADIO    COMMUNICATION. 

When  a  direct  current  ammeter  is  traversed  by  an  ordinary  alter- 
nating current,  the  changes  of  current  are  altogether  too  rapid  to  be 
followed  by  the  needle  of  the  instrument.  It  can  only  take  up  an 
average  position  corresponding  to  the  average  of  all  the  values 
through  which  the  current  passes  during  a  cycle.  However,  since 
the  current  passes  through  the  same  values  in  one  direction  that  it 
does  in  the  other,  the  average  value  during  the  cycle  must  be  zero. 
That  this  is  the  case  can  be  shown  by  connecting  a  direct  current 
ammeter  into  an  alternating  current  circuit.  The  ammeter  needle 
stands  still  at  zero,  or  else  merely  presents  a  blurred  appearance 
while  standing  at  zero.  The  same  remarks  apply  to  the  use  of  a 
d.c.  voltmeter  in  an  a.c.  circuit. 

A. C.  Voltmeters  and  Ammeters  Indicate  Effective  Values. — Alternat- 
ing current  voltmeters  and  ammeters  may  be  of  several  different 
types  (hot  wire,  dynamometer  or  electrostatic,  see  Sec.  60),  all 
of  which,  however,  give  a  deflection  in  the  same  direction  which- 
ever the  direction  of  the  current.  The  force  on  the  moving  portion 
of  such  an  instrument  is,  at  every  moment,  proportional  to  the 
square  of  the  current  through  the  instrument.  When  an  alternat- 
ing current  passes,  the  average  deflection  taken  up  by  the  pointer 
is,  therefore,  proportional  to  the  average  of  the  squares  of  all  the 
values  of  current  during  the  cycle.  For  a  true  sine  current,  the 
average  of  the  squares  of  all  the  values  of  current  during  the  cycle 
can  be  shown  to  have  a  value  of  one-half  the  square  of  the  maximum 
value. 

Equivalent  Direct  Current. — The  heating  effect  of  a  current  is,  at 
every  moment,  proportional  to  the  square  of  its  value  at  that  moment. 
The  average  heating  effect  of  an  alternating  current  must,  therefore, 
be  proportional  to  the  average  of  the  squares  of  all  the  values  of  the 
current  during  the  cycle,  or  must  be  proportional  to  one-half  the 
square  of  the  maximum  current.  The  same  heating  effect  would,  of 
course,  be  produced  by  a  steady  current,  whose  square  is  equal  to 
the  average  of  the  squares  of  the  alternating  current  taken  over  the 
whole  cycle.  That  is,  the  "effective  current"  is  equal  to  the  value 
of  the  direct  current  which  would  produce  the  same  heating  effect 
in  the  circuit  in  question.  Since  its  square  is  equal  to  one-half  the 
square  of  the  maximum  value,  the  effective  value  of  the  current  is 


T__    /(maximum)2 

O 


RADIO   COMMUNICATION.  97 

or  equal  to  the  maximum  value  divided  by  -\/2.  This  is  the  same  as 
the  maximum  value  multiplied  by  0.707. 

The  effective  current  in  the  table  above  is  7.07  amp.,  and  this 
would  be  the  current  indicated  by  an  a.c.  ammeter  in  the  circuit, 
although  the  current  varies  between  10  amp.  in  one  direction  and  10 
in  the  other.  The  same  heating  effect  would  result  if  a  direct  cur- 
rent of  7.07  amp.  were  sent  through  the  circuit.  Likewise,  an  a.c. 
voltmeter  will  always  read  the  effective  value  of  the  voltage,  which 
is  equal  to  the  maximum  voltage  multiplied  by  0.707. 

52.  Circuit  with  Resistance  Only.  —  Let  us  imagine  a  circuit  with 
resistance  R  ohms,  and  with  such  small  inductance  and  capacitance 
that  they  may  be  neglected.  Let  us  suppose,  further,  that  sine 
wave  alternating  emf.  is  applied  to  the  circuit.  At  every  moment, 
the  current  will  be  found  by  dividing  the  emf.  at  that  instant  by 
the  resistance  of  the  circuit.  The  current  is  zero  at  those  moments 
when  the  emf.  is  also  zero,  and  is  a  maximum  when  the  emf.  is  a 
maximum.  In  fact,  the  changes  of  current  keep  step  with  those  of 
emf.  The  current  and  emf.  are  said  to  be  "in  phase"  or  to  have 
"zero  phase  angle."  Since  the  effective  values  of  'emf.  and  current 
are  each  the  same  fraction  of  their  respective  maximum  values,  the 
effective  current  /  will  be  calculated  from  the  effective  emf.  E  by 
the  relation 


That  is,  in  this  special  case,  Ohm's  law  holds,  even  when  the  cur- 
rent ip  alternating.  An  ordinary  incandescent  lamp  circuit  approx- 
imates this  ideal  circuit. 

The  power  in  the  circuit  is,  at  every  moment,  equal  to  the  product 
of  the  values  of  current  and  emf.  which  hold  at  that  moment.  The 
average  power  taken  over  the  whole  cycle  is  equal  to  the  product  of 
the  effective  current  by  the  effective  emf.  ,  that  is,  average  P=IE. 
The  power  is  used  up  in  the  circuit  entirely  in  heating  the  resistance 
R. 

53.  Phase  and  Phase  Angle.  —  The  values  of  current  given  in  the 
table  above  are  those  which  hold  for  certain  definite  moments  in  the 
cycle  of  change  of  the  current.  Each  time  the  cycle  is  repeated, 
the  same  values  are  run  through,  and  any  chosen  value  will  be 
reached  at  a  perfectly  definite  fraction  of  the  way  through  the  cycle. 
Each  maximum  in  the  positive  direction,  for  example,  occurs  just 
97340°  —  19  -  7 


98  RADIO    COMMUNICATION. 

one-quarter  of  a  cycle  after  the  preceding  zero  value.  The  points  A 
in  Fig.  71  have  the  same  phase,  although  each  is  in  a  different  cycle 
from  the  others.  The  current  has  the  same  value  at  the  points  C 
as  at  A,  but  points  C  are  not  in  the  same  phase  as  A,  since  at  A  the 
current  is  increasing,  and  at  C  it  is  decreasing. 

The  phase  is,  then,  a  certain  aspect  or  appearance,  occurring  at 
the  same  definite  part  of  each  succeeding  cycle.  Difference  in 
phase  is  nothing  more  than  difference  in  position  in  the  cycle.  It 
is  best  referred  to  as  difference  in  time,  expressed  as  the  fraction  of 
the  length  of  a  cycle.  Thus,  the  difference  of  phase  of  points  B  and 

0,  Fig.  71,  is  one-quarter  of  a  cycle;  that  of  points  B  and  D  one-half 
cycle,  etc.     It  is  also  customary  to  express  difference  in  phase  as  an 
angle.    A  difference  of  phase  of  one  complete  cycle  is  regarded  as 
equivalent  to  the  angle  of  a  whole  revolution  or  circumference,  that 
is,  to  360°.     One-quarter  cycle  is  accordingly  90°,  and  two  points 
with  a  difference  of  phase  of  one-quarter  cycle  are  said  to  have  a 
difference  of  phase  of  90°,  etc. 

The  idea  of  phase  angle  is  useful  when  two  emfe.  are  acting 
in  the  same  circuit  or  when  the  current  and  the  emf.  which  pro- 
duces it  do  not  pass  through  their  maxima  at  the  same  moment. 
Fig.  72  shows  the  waves  of  emf.  and  current  in  a  circuit  where  the 
emf.  and  current  differ  in  phase  by  about  one-eighth  of  a  cycle; 

1.  e.,  they  have  a  phase  angle  of  about  45°. 

When  a  circuit  has  resistance  but  no  inductance  or  capacitance, 
the  emf.  and  current  are  in  phase  or  the  phase  angle  is  zero.  Their 
waves,  shown  in  Fig.  73,  pass  through  zero  at  the  same  moments 
and  reach  their  maximum  values  at  the  same  moments. 

The  case  of  opposite  phase  shown  in  Fig.  74,  in  which  two  emfs. 
are  represented,  is  such  that,  although  they  pass  through  their  zero 
values  at  the  same  moments,  at  other  times  one  is  always  acting  in 
the  opposite  direction  to  the  other.  Their  phase  angle  is  180°. 

In  any  series  circuit  where  the  reactance  is  not  zero  the  applied 
emf.  and  the  current  have  a  difference  of  phase. 

54.  Alternating  Current  in  a  Circuit  Containing  Inductance  Only. — 
Such  a  circuit  would  be  approximately  represented  by  one  with  a 
large  inductance  coil  wound  with  such  large  wire  that  only  a  very 
small  resistance  would  be  offered  to  the  current. 

If  an  alternating  emf.  is  applied  to  the  circuit,  an  alternating 
current  flows,  and  the  changes  of  the  current  induce  an  emf.  in  the 
circuit  which  is  greater,  the  greater  the  inductance  and  the  more 


RADIO   COMMUNICATION. 


99 


rapidly  the  current  changes;  that  is,  the  greater  the  frequency  of 
the  current. 

The  current  i  changes  most  rapidly  at  the  points  -4,  B,  and  C, 
Fig.  75,  where  it  is  passing  through  zero  value.  The  induced  emf. 
must  therefore  be  a  maximum  at  those  points.  Since  it  always 
opposes  the  change  of  current,  it  must  be  at  its  maximum  negative 
value  in  the  figure  at  the  points  of  the  axis,  A  and  C,  and  at  its 
positive  maximum  at  point  B.  At  points  D  and  E,  the  current  does 
not  change  for  a  moment,  so  that  the  induced  emf.  must  be  zero  at 


Lmf.  And    current  curves    with 
A    difference,    of  (ahdae  of  *S 


d   current  curves 


Fia  14 

Two    emf.  curves   m 


torrent"    M 
tndoctive     circuit 


those  times.  It  is  not  difficult  to  show  that  when  we  have  a  sine 
alternating  current  there  is  also  a  sine  alternating  emf.  induced  as 
shown  in  curve  e,  Fig.  75. 

In  this  kind  of  a  circuit,  this  induced  emf.  has  to  be  overcome 
at  each  moment,  but  the  applied  emf.  is  not  requisitioned  for  any 
other  service.  Accordingly  the  applied  and  induced  emfs.  are  at 
every  moment  equal  and  opposite.  The  applied  emf.  wave  is 
therefore  given  by  curve  v,  Fig.  75,  drawn  with  its  vertical  heights 
just  equal  and  opposite  to  those  of  the  curve  e.  It  is  evident  that 


100  RADIO    COMMUNICATION. 

the  current  lags  one-quarter  of  a  cycle  in  its  changes  behind  those 
of  the  applied  emf .  The  current  is  said  therefore  to  lag  90°  in  phase 
behind  the  applied  emf. 

The  effective  value  of  the  induced  emf.  can  be  shown  to  have  the 
value  27T/L7,  in  which  /  is  the  frequency,  L  the  inductance  in 
henries,  I  the  effective  value  of  the  current  in  amperes,  and  ir= 
3.1416,  or  nearly  3|.  An  effective  applied  emf.  E,  therefore,  will 
produce  a  current  whose  effective  value  is 


Inductive  Reactance. — The  quantity  X=2.irfL  is  known  as  the 
reactance  of  the  inductance  coil.  It  is  larger,  the  greater  the  fre- 
quency and  the  greater  the  inductance,  as  would  be  expected,  and 
has  a  considerable  value  in  many  cases.  The  reactance  is  measured 
in  ohms.  As  an  example,  suppose  a  coil  of  0.1  henry  at  100,000 
cycles  per  sec.  The  reactance  is  ^=6.283X100,000X0.1=62,830 
ohms.  That  is,  such  a  circuit  throttles  down  the  current  as  much 
as  a  resistance  of  62,830  ohms  would  do.  There  is  this  difference, 
however,  between  the  effects  of  an  inductance  and  a  resistance,  that 
no  energy  is  dissipated  in  heat  in  an  inductance.  In  one-half  of  the 
cycle  energy  is  taken  from  the  circuit,  it  is  true,  but  this  is  stored 
up  in  the  magnetic  field  around  the  coil,  and  in  the  next  half  cycle 
the  magnetic  field  collapses  on  the  coil  and  gives  the  energy  back 
to  the  circuit.  Thus,  in  the  long  run,  energy  is  neither  gained  nor 
lost  in  the  circuit.  . 

55.  Circuit  Containing  Inductance  and  Resistance  in  Series. — It  is, 
of  course,  impossible  to  arrange  a  circuit  which  has  absolutely  no 
resistance.  In  addition  to  overcoming  the  induced  emf.,  a  portion 
of  the  applied  emf.  has  to  be  employed  to  force  the  current  through 
the  resistance  of  the  circuit.  Thus,  if  the  current  at  any  moment 
is  passing  through  the  value  i,  the  emf.  necessary  to  force  the  cur- 
rent through  the  resistance  is  Ri,  and  that  which  is  overcoming  the 
induced  emf.  is  Xi,  so  that  the  value  e  which  the  applied  emf.  has 
at  that  moment  is  e=Ri-\-Xi.  This  equation  shows  the  simple  and 
obvious  connection  between  the  value  of  the  current  at  any  instant, 
and  the  corresponding  instantaneous  value  of  the  emf.  which  is 
producing  it.  However,  it  cannot  be  used  to  calculate  the  effective 
current  from  the  effective  applied  voltage,  for  the  reason  that  the 
two  emfs.  Ri  and  Xi  are  not  in  phase.  When  the  former  is  passing 
through  zero  value,  the  latter  is  at  its  maximum  and  vice  versa,  so 


RADIO  COMMUNICATION* 


that  the  sum  of  the  two  emfs.  has  a  maximum  valute  less  than 'the 
sum  of  their  individual  maximum  values. 

This  is  in  line  with  the  results  of  the  following  experiment.  Let 
a  coil  of  inductance  L  be  joined  in  series  with  a  resistance  R,  and 
let  three  voltmeters  a,  b,  and  c  be  applied,  as  shown,  Fig.  76,  to 
measure  the  emf.  between  the  points  A  and  B,  B  and  C,  and  A  and 
C.  The  voltages  measured  by  the  voltmeters  are  effective  values, 
and  it  is  found  that  the  reading  of  c  is  not  equal  to  the  sum  of  the 
readings  of  a  and  6  as  would  be  the  case  with  a  direct  current. 

The  voltmeter  a  gives  the  emf.  RI  and  the  voltmeter  6  the  emf. 
XI,  where  /  is  the  effective  value  of  the  current,  which  would  be 
measured  by  an  a.c.  ammeter  in  the  circuit.  Analysis  shows  that 


E.      (b) 


Circuit   with    inductince  And  resistance 


is.4 


F  (  a  -n 


E-mf.  an<J  im>«<^An 
for  circuit  having 
And  mJucfciMce 


l<3. 79 
Volfc^e 

e.-  too 


the  reading  E  of  the  voltmeter  c  is  represented  by  the  hypotenuse 
of  the  right  triangle  whose  sides  are  RI  and  XI.     See  Fig.  77-a. 

The  effective  applied  emf.  E  in  such  a  case  is  therefore  related 
to  the  voltages  RI  and  XI  by  the  equation  (relation  between  sides 
and  hypotenuse  of  a  right  triangle), 


(X2+R2) 


(59) 


Accordingly,  the  effective  value  of  the  current  produced  by  the 
effective  applied  emf.  E  is 

(60) 


102     ^  w  ..        RAPIO,  COMMUNICATION. 


.— ^'Hi^quantity  V-^2+^2  is  known  as  the  "  impedance  " 
of  the  circuit.  It  takes  the  place  in  alternating  current  theory  of 
the  resistance  in  Ohm's  law.  It  is  related  to  the  resistance  and 
reactance  as  the  sides  of  the  right  triangle,  Fig.  77-b. 

As  an  example,  suppose  in  Fig.  78  that  L=Q.l  henry,  R=IQ  ohms, /=  CO  cycles 
per  second.  Find  what  applied  emf.  is  necessary  to  cause  an  effective  current  of 
2  amp.  to  flow. 

.R  7  =  20  volts 

X  =6.283X60X0. 1=37.7  ohms 
XI=  75.4  volts. 
The  applied  emf.  must  therefore  be  by  (59) 

E=  V(20)2+(75.4)2=78.0  volts. 

The  reverse  problem  is  to  find  what  current  will  flow  in  the  circuit,  when  a  given 
emf.,  say  100  volts,  is  applied.     The  impedance  is   ~JR'*+X2=  V(10)2+(37-7)2= 
39  ohms. 
Therefore  the  current  will  be  12P_=2.5c  amp.    The  emf.  on  the  resistance  is  2.56X 

10=25.6  volts  and  that  on  the  reactance  2.56X37.7=95.5  volts,  so  that  the  voltage 
triangle  is  that  given  in  Fig.  79. 

Power  Factor. — The  power  dissipated  in  heat  in  this  circuit  is  of 
course  I2JS=(2.56)2X10=65.5  watts.  The  product  of  the  effective 
current  and  effective  voltage  is  100X2.56=256  "  volt-amperes. " 
To  obtain  the  dissipated  power  from  this  product,  it  is  therefore 

necessary  to  multiply  by  "25^ = 0.256.     Note  that  this  is  the  same  as 

og-^j  — •   The  number  which  it  is  necessary  to  multiply  into  the 

product  of  volts  and  amperes,  in  order  to  get  the  power,  is  called 
the  "power  factor.  "  The  power  factor  of  the  above  circuit  is  0.256. 
A  circuit  with  resistance  only  and  no  inductance  or  capacitance  has 
a  power  factor  of  1.  A  resonant  circuit  (see  Chap.  4)  is  another  ex- 
ample of  power  factor  equal  to  1 .  The  power  factor  ia  other  cases 
always  lies  between  zero  and  one.  The  power  in  any  circuit  is  cal- 
culated, then,  by  the  formula 

P=EIF  (61) 

the  power  factor  being  given  by  the  general  formula 

resistance 
impedance 

56.  Charging  of  a  Condenser  in  an  Alternating  Current  Circuit. — 
A  steady  emf.  is  not  able  to  pass  a  steady  current  through  a  condenser. 
When  the  circuit  is  first  closed,  a  charging  current  flows  into  the 


RADIO  COMMUNICATION. 


103 


condenser,  until  the  voltage  between  the  plates  of  the  latter  has 
risen  to  the  same  value  as  the  applied  voltage.  If  the  voltage  is 
removed  and  the  circuit  completed  by  a  wire,  a  discharge  current 
flows  out  of  the  condenser  in  the  opposite  direction  to  the  charging 
current.  The  discharge  ceases  when  the  plates  of  the  condenser 
have  no  potential  difference.  (See  Sec.  30.) 

With  an  alternating  emf .  in  the  condenser  circuit,  an  alternating 
current  is  constantly  flowing  into  and  out  of  the  condenser  to  keep 
the  voltage  between  the  plates  equal  to  the  instantaneous  value  of 
the  applied  emf.  The  current  is  largest  at  those  moments  when  the 
applied  emf.  is  changing  most  rapidly;  it  is  zero  at  the  moments 
when  the  emf.  is  for  a  moment  stationary  at  its  maximum  values. 
If  curve  e,  Fig.  80,  re  presents  a  sine  alternating  emf.,  it  can  be  shown 
that  the  charging  current  curve  will  be  like  curve  i;  that  is,  the 


Emf. And  cKar-Wnk  current  in  condenser 
e  circuit. 

i-y 

Ficj.So  A 


Current  drvd  «mfo.on  co'il  «»nd  condenser 


Voltaic  <»rvJ    impedance   Tria 
circu.t    with     fc,L  and  C 


charging  current  is  90°  "ahead  "  of  the  applied  emf.  in  phase.  (Con- 
trast this  with  the  relations  in  the  inductive  circuit.)  The  charging 
current  will,  in  general,  be  greater  the  greater  the  capacitance  (7, 
and  the  greater  the  frequency  of  the  emf. 

Reactance  of  Condenser. — Analysis  shows  that  the  effective  value  / 
of  the  charging  current  is  /=  2wfCE.  The  reactance  of  the  condenser 
is  accordingly 


where  C  is  the  capacitance  in  farads.  This  shows  that  the  reactance 
of  the  condenser  is  greater,  the  smaller  the  capacitance  and  the  lower 
the  frequency.  (Contrast  with  the  reactance  of  an  inductance.) 
The  reactance,  as  before,  is  measured  in  ohms. 


104  RADIO    COMMUNICATION. 

As  an  example,  we  find  that  the  reactance  of  a  condenser  of  0.1 
mfd.  at  60  cycles  is 

106 
6.283X60X0.1=26'500ohms- 

At  100,000  cycles,  the  reactance  is  only  15.9  ohms.  From  this  it 
appears  that  the  condenser  offers  much  less  obstruction  to  flow  of 
current  at  high  frequency  than  at  low  frequency,  and  hence,  that  a 
given  alternating  emf.  causes  a  much  larger  current  flow,  if  the 
.alternations  are  rapid,  than  if  they  are  slow. 

No  energy  is  dissipated  in  a  perfect  condenser.  Energy  is  stored 
in  the  dielectric  of  the  condenser  while  it  is  being  charged,  but  this 
is  all  restored  to  the  circuit  when  the  condenser  discharges.  Actu- 
ally, no  condenser  is  perfect,  although  well  designed  air  condensers 
may  be  regarded  as  essentially  so.  Heat  is  always  dissipated  to  a 
measurable  extent  in  condensers  with  solid  dielectrics.  The  con- 
denser acts  as  though  a  certain  resistance  were  joined  in  series  with 
it.  The  actual  value  of  this  suppositions  series  resistance  depends 
upon  the  capacitance  and  the  frequency,  as  well  as  upon  the  nature 
of  the  dielectric.  It  is  less,  the  greater  the  capacitance  and,  in 
general,  inversely  proportional  to  the  frequency. 

57.  Circuit  Containing  Capacitance,  Inductance  and  Resistance 
in  Series.  —  When  an  inductance  and  capacitance  are  joined  in  series 
and  subjected  to  an  alternating  emf.,  the  current  through  them  both 
is  the  same  and  the  emf.  on  the  condenser  is  Xci  and  that  on  the  in- 
ductance Xrf,  where  the  instantaneous  current  has  the  value  i,  XL  is 
the  reactance  of  the  coil  and  Xc  the  reactance  of  the  condenser.  The 
curves  for  these  voltages  may  be  derived  by  combining  the  curves 
of  Figs.  75  and  80.  The  curves  XLi  and  Xci,  Fig.  81,  show  that 
at  every  moment  the  voltage  on  the  condenser  opposes  that  on  the 
inductance.  The  circuit  acts  as  though  it  possessed  a  single  react- 
ance equal  to  the  difference  of  the  reactance  of  the  coil  and  the  react- 
ance of  the  condenser.  If  the  latter  is  the  larger,  the  circuit  behaves 
like  a  condenser  circuit,  and  if  the  coil  has  the  greater  reactance, 
the  circuit  behaves  like  an  inductive  circuit. 

The  effective  values  of  the  voltages  in  the  circuit  are  shown  in 
Figs.  82-a  and  b.  The  impedance  is  found  by  combining  the  resist- 
ance and  the  resulting  impedance  in  the  triangle  diagram  of  Fig. 
82-c.  The  value  of  the  impedance  is  evidently 


(64) 


RADIO   COMMUNICATION. 


105 


58.  The  Alternating-Current  Transformer. — Remembering  the 
principles  of  induced  currents  in  Section  45,  it  is  evident  that  when 
an  alternating  current  is  flowing  in  a  circuit,  the  alternating  magnetic 
field  will  cut  in  and  out  through  any  neighboring  circuit,  and  induce 
an  alternating  emf.  in  the  latter.  This  induced  emf.  will  depend 
upon  the  mutual  inductance  of  the  two  circuits  (Sec.  47)  the  cur- 
rent in  the  inducing  circuit,  and  the  frequency  of  this  current.  It 
can  be  shown  that,  if  /  is  the  effective  value  of  the  current,  M  the 
mutual  inductance  and  /  the  frequency,  the  effective  value  of  the 
emf.  induced  will  be  2-nfMI.  In  low-frequency  work,  Mis  made  as 
large  as  possible  by  winding  the  two  circuits  on  an  iron  form,  so  that 
almost  all  of  the  magnetic  flux  produced  by  the  current  passes 
through  the  second  circuit.  This  arrangement  is  called  a  "trans- 
former." (See  Fig.  83.)  The  induced  voltage  is  to  the  applied 
voltage  in  the  ratio  of  the  number  of  turns  on  the  two  coils,  the  larger 
voltage  being  found  in  the  circuit  which  makes  the  greater  number 


Fia.64 

Fia.6 

3 

^ 

« 

A 

• 

3 

< 

1 

s: 
& 

Ti'mo 

_--—_"-- 

~-p\ 

Pul.S<rKn&      Current 

im 

>le    Transf 

orm 

«r 

of  turns  around  the  iron.  Thus,  if  one  coil  has  1000  turns  and  the 
other  100,  and  an  emf.  of  200  volts  is  applied  to  the  latter,  an  emf. 
of  2000  volts  is  induced  in  the  former.  When  current  is  drawn  from 
the  second  circuit,  it  is  found  that  the  currents  in  the  two  circuits 
are  nearly  in  the  ratio  of  the  numbers  of  turns,  the  greater  current 
being  found  in  the  lower  voltage  circuit. 

At  radio  frequencies,  the  effectiveness  of  iron  in  increasing  the 
magnetic  flux  is  not  so  great  as  at  low  frequencies.  (See  Sec.  42, 
foot-note.)  To  increase  the  mutual  inductance,  the  coils  are  made 
large  and  are  brought  near  each  other.  Usually  no  iron  core  is 
employed.  For  a  further  treatment,  see  Section  121  on  coupled 
circuits. 

A  common  use  of  a  transformer  with  radio  frequencies  is  to  obtain 
an  alternating  current  from  a  pulsating  current.  For  example  in 
the  use  of  vacuum  tubes  for  amplifying  received  signals,  Section  194, 
Chapter  8,  pulsations  are  produced  in  the  plate  current,  above  and 


106  RADIO    COMMUNICATION. 

below  its  normal  steady  value.  By  passing  the  plate  current 
through  the  primary  of  a  transformer,  an  amplified  alternating  emf. 
is  obtained  in  the  secondary,  and  this  emf.  is  applied  to  the  grid 
circuit  of  a  second  vacuum  tube,  and  so  on.  If  curve  a,  Fig.  84, 
represents  a  pulsating  current,  the  latter  may  evidently  be  regarded 
as  compounded  of  a  steady  current  (dotted  line)  and  an  alternating 
current.  The  steady  current  has  no  inducing  effect  in  the  trans- 
former, but  the  alternating  part  induces  an  alternating  emf.  in  the 
secondary  circuit. 

J.  Measuring  Instruments. 

From  what  has  gone  before,  it  will  be  plain  that  the  presence  of  an 
electric  current  can  be  known  by  such  effects  as  the  production  of 
heat,  magnetic  action,  or  chemical  changes.  All  of  these  effects  are 
greater  with  a  strong  current  than  with  a  weak  one,  therefore  all  can 
be  used  to  give  an  idea  of  the  magnitude  of  a  current.  Instruments 
have  been  invented  which  take  advantage  of  each  of  those  effects, 
but  some  are  more  conveniently  used  than  others.  Those  about 
which  the  student  of  radio  particularly  needs  to  know  are  based  on 
two  effects  of  the  electric  current;  the  magnetic  effect  and  the  heat- 
ing effect. 

Meters  can  be  used  either  to  indicate  the  current  in  amperes  flow- 
ing in  a  circuit,  in  which  case  they  are  called  ammeters,  or  to  indicate 
the  potential  difference  in  volts  between  two  points,  in  which  case 
they  are  voltmeters. 

59.  Hot  Wire  Instruments. — Currents  of  radio  frequency  are  gen- 
erally measured  by  means  of  instruments  which  depend  on  the  heat- 
ing of  a  wire  or  strip  of  metal.  They  are  therefore  called  "thermal" 
ammeters.  These  are  again  divided  into  two  main  classes,  the 
expansion  and  the  thermocouple  instruments.  The  first  takes 
advantage  of  the  lengthening  of  a  metal  wire  or  strip  when  it  is  heated. 
Fig.  85  illustrates  the  principle.  The  current  to  be  measured 
flows  along  the  wire  AB,  which  is  of  a  material  having  sufficient 
resistance  to  cause  it  to  become  hot.  In  heating,  it  stretches  some- 
what. That  permits  it  to  be  pulled  aside  by  the  spring  S  acting 
through  the  thread  T.  The  latter  passes  around  the  shaft  P,  and  by 
turning  it  causes  the  pointer  to  move  over  the  scale  a  greater  or  less 
distance,  depending  on  the  current  in  AB.1  The  scale  is  graduated 
(marked  off)  in  amperes  so  that  the  position  of  the  pointer  shows 
directly  how  large  the  current  is. 

1  This  principle  is  used  in  meters  made  by  the  General  Radio  and  Roller-Smith  Cos. 


RADIO   COMMUNICATION.  107 

The  thermocouple  type  of  ammeter  J  utilizes  the  fact  that  when  the 
junction  of  two  dissimilar  metals  is  heated,  an  emf.  is  developed  (see 
Sec.  15).  A  pair  of  metals  used  for  this  purpose  is  called  a  "ther- 
mocouple." The  value  of  the  emf.  depends  on  the  combination  of 
metals  and  ordinarily  increases  directly  as  the  temperature  is 
increased. 

In  Fig.  86,  the  thermocouple  consists  of  the  two  wires  c  and  d, 
and  their  junction  is  in  contact  with  the  hot  wire  AB,  in  which  the 
radio  frequency  current  is  flowing.  The  emf.  produced  by  the 
heat  at  the  junction  is  applied  to  G,  an  instrument  of  the  type  shown 
in  Fig.  88  below,  and  causes  a  pointer  to  deflect;  the  millivoltmeter 


FIQ.&S 


•>cif>le     of  Thermal  Ammeter 
mX    Thermocouple 


G  responds  to  the  direct  current  sent  through  it  by  the  emf.,  as  will 
be  explained  in  the  next  section. 

It  is  to  be  noted  that  the  heat  due  to  a  given  number  of  amperes 
of  alternating  current  is  the  same  as  that  of  an  equal  number  of 
amperes,  direct  current.  In  fact,  an  ampere  is  defined,  in  alter- 
nating currents,  as  being  such  a  current  that  the  heat  it  produces 
in  a  given  conductor  is  the  same  as  is  produced  by  1  amp.,  direct 
current.  (See  Sec.  51.)  The  emf.  produced  at  the  junction  does 
not  depend  on  the  direction  of  the  current  in  AB,  but  merely  on 
the  amount  of  heat  produced.  This  emf.  is  always  in  the  same 
direction;  it  can  therefore  be  measured  by  a  d.c.  instrument.  Thus 
the  combination  is  useful  for  measuring  high  frequency  currents. 

The  heat  developed  varies  as  the  square  of  the  current,  and  the 
emf.  of  the  thermocouple  varies,  quite  closely,  as  the  heat 

i  Such  instruments  are  made  by  the  Western  Electrical  Instrument  Co.  and  the 
Roller-Smith  Co. 


108  RADIO    COMMUNICATION. 

developed,  so  the  indications  of  ammeters  of  the  thermal  type 
change,  practically,  as  the  square  of  the  current.  Consequently 
the  scale  is  not  uniform,  being  more  open  at  the  upper  end  than  at 
the  lower. 

In  Fig.  86  the  thermocouple  is  made  to  appear  separate  from  the 
rest  of  the  instrument;  in  commercial  ammeters  the  thermocouple 
and  the  indicating  instrument  are  placed  inside  the  same  case,  and 
the  scale  is  made  to  read  the  amperes  in  the  radio  frequency  circuit. 

When  a  hot  wire  instrument  is  needed  for  currents  of  more  than  a 
few  amperes,  it  is  not  practicable  to  build  it  with  a  single  heating 
wire.  This  is  true  both  for  expansion  and  for  the  thermocouple 
type.  Several  hot  wires  or  strips  are  therefore  used,  arranged  cylin- 
drically  so  that  the  radio  currents  divide  equally  among  them. 
Then,  either  the  effect  on  one  of  them  alone  is  used  to  operate  the 
indicating  mechanism,  or  if  thermocouples  are  used,  the  emfs.  of 
several  can  be  combined  in  series,  so  that  their  effects  are  added. 

On  some  of  the  older  radio  equipments,  instruments  are  found 
which  are  incorrectly  called  wattmeters.  They  are,  as  a  matter  of 
fact,  simply  ammeters  in  which  the  scale,  instead  of  being  marked  in 
amperes,  is  marked  proportionally  to  the  square  of  the  number  of 
amperes.  They  are  properly  called  "current-square  meters." 

60.  Magnetic  Instruments.— While  the  heating  effect  of  the  cur- 
rent is  used  for  measurements  at  radio  frequency,  the  magnetic 
effect  is  the  one  utilized  in  most  instruments  for  direct  and  for  low 
frequency  alternating  current.  The  simplest  and  most  common 
instrument  for  measuring  direct  current  depends  upon  the  force 
between  a  permanent  magnet  and  wire  carrying  current. 

D.  C.  Milliammeter. — Fig.  87  represents  a  rectangular  coil  C  of 
fine  insulated  wire  between  the  poles  NS  of  a  permanent  mag- 
net.1 The  coil  consists  of  a  number  of  turns  wound  on  a  light  metal 
frame,  which  is  pivoted  in  jewel  bearings  like  those  of  a  watch. 
SS  are  spiral  springs  resembling  the  hairspring  of  a  watch,  but 
somewhat  heavier  and  made  of  material  that  is  a  better  electrical 
conductor  than  steel.  They  serve  the  double  purpose  of  conduct- 
ing the  current  and  controlling  the  position  of  the  coil.  0  is  a  cylin- 
drical piece  of  soft  iron  that  serves  as  a  good  magnetic  path  between 
N  and  S,  and  causes  a  strong  and  uniform  magnetic  field  to  exist 
in  the  spaces  between  N  and  0,  and  between  0  and  S. 

i  Instruments  with  a  movable  coil  in  the  field  of  a  permanent  magnet  arc  called  the 
"moving-coil"  type. 


RADIO   COMMUNICATION. 


109 


Assume  that  A  and  B  are  connected  to  a  source  of  emf.,  so  that 
current  flows  as  indicated  by  the  arrows.  In  the  portion  of  the 
coil  next  to  the  N  pole  of  the  magnet  the  current  flows  downward 
in  each  turn  of  wire.  The  direction  of  the  magnetic  field  is  always 
from  N  toward  S.  By  the  "left-hand  rule"  (Sec.  43),  it  is  seen 
that  the  force  on  the  wires  is  toward  the  front  (out  of  the  paper). 
On  the  side  of  the  coil  near  the  S  pole  the  current  is  up;  that  side 
tends  to  be  pushed  toward  the  rear  (into  the  paper).  As  a  whole, 
therefore,  the  coil  tends  to  turn  on  its  pivots.  This  motion  is  opposed 


FIG 


Fia.85 


Principle  of  the  Milliammeter 


Principle    /-*  Ammeter   Conn«c.tior 


Principal    Rarrs'of  FC    Voltmeter 
.and  Ammeter 


by  the  springs,  and  for  each  strength  of  current,  there  is  some  posi- 
tion of  the  coil  in  which  the  force  due  to  the  current  and  the  force 
due  to  the  springs  balance.  A  pointer  can  therefore  be  attached  to 
the  coil  so  as  to  indicate,  by  its  position  over  a  scale,  the  current 
in  amperes,  in  the  coil.  With  the  strong  magnets,  delicate  parts, 
and  fine  workmanship  found  in  good  instruments,  it  takes  only  a 
very  small  fraction  of  an  ampere  to  move  the  pointer  over  its  entire 
range;  the  scale  may  be  graduated  in  thousandths  of  an  ampere 


110  RADIO    COMMUNICATION. 

and  the  instrument  used  as  a  "milliammeter."  Also,  with  certain 
modifications  to  be  described  presently,  the  instrument  can  be 
used  to  indicate  millivolts,  and  is  then  called  a  "milli  voltmeter." 

The  arrangement  of  the  parts  of  such  an  instrument  is  shown  in 
Fig.  88.  Attached  to  the  ends  of  the  permanent  magnet  MM  are 
the  soft  iron  pole-pieces  NS,  and  between  them  is  the  cylindrical 
soft  iron  core  0,  mounted  on  supports  not  shown  in  the  sketch. 
This  arrangement  provides  a  strong  and  uniform  magnetic  field  in 
the  narrow  gap  G.  The  coil  C  is  free  to  turn  in  this  gap,  which  is 
wide  enough  merely  to  allow  the  necessary  clearance.  P  is  the 
upper  spiral  spring,  above  the  top  of  the  coil.  The  other  one  is 
under  the  core  0.  The  pointer  is  a  thin  tube  of  aluminum,  flattened 
at  the  end.  The  whole  is  inclosed  in  a  dust  tight  case,  with  a  glass 
over  the  scale.  From  the  description  it  should  be  evident  that 
abuse,  such  as  setting  the  meter  down  with  a  jar,  or  applying  exces- 
sive currents,  will  ruin  it. 

Moving  Coil  Galvanometer. — For  very  delicate  measurements, 
where  even  a  milliameter  is  not  sensitive  enough,  the  pivots  and 
springs  are  done  away  with  and  the  coil  is  suspended  by  a  long  fine 
wire  or  strip,  which  conducts  the  current  to  it  and  at  the  same  time 
opposes  the  turning  effort  due  to  the  current.  Another  fine  wire  at 
the  bottom  provides  the  other  connection  to  the  coil.  If  the  sus- 
pension wire  is  fine  enough  and  the  coil  has  many  turns,  such  an 
instrument,  called  a  " moving  coil  galvanometer,"  can  be  used  to 
measure  currents  less  than  a  millionth  of  an  ampere.  No  pointer  is 
used;  a  tiny  mirror,  attached  to  the  coil,  changes  the  direction  of 
light  reflected  from  it  as  the  coil  turns. 

Ammeters. — An  instrument  of  the  type  of  Fig.  88  can  be  built 
only  for  small  currents,  otherwise  the  coil  and  other  parts  would  be 
so  huge  as  to  be  unwieldy.  For  larger  currents  the  scheme  of  Fig. 
89  is  used.  The  current  in  A  is  to  be  measured.  S  is  a  short  resistor 
called  a  "shunt,"  consisting  of  one  or  several  strips  of  a  special  alloy 
large  enough  to  carry  the  current. 

The  current  divides,  most  of  it  going  through  S,  because  its  resist- 
ance is  small.  A  little  of  it  flows  through  the  millivoltmeter  M,  of 
which  the  resistance  is  large  compared  with  S.  This  current  in 
M,  though  small,  is  a  perfectly  definite  fraction  of  the  total  (Sec.  25); 
therefore,  if  we  know  how  great  it  is,  we  can  know  at  once  how  great 
the  total  is. 


RADIO  COMMUNICATION.  Ill 

For  example,  if  the  resistance  of  S  is  0.01  ohm  and  that  of  M  is 
0.99,  then  the  current  divides  in  the  same  ratio,  the  larger  part  flow- 
ing in  the  path  of  smaller  resistance.  Out  of  every  unit  of  current 
0.99  flows  by  way  of  S  and  only  0.01  passes  through  the  millivolt- 
meter.  The  total  is  100  times  as  great  as  the  current  in  M.  If  the 
resistances  are  0.001  and  0.999,  then  the  total  is  1000  times  as  great. 
The  small  current  in  the  meter  is  an  accurate  measure  of  the  much 
larger  current  in  A;  for  any  one  shunt  the  scale  is  therefore  made  to 
read  directly  in  amperes  of  total  current. 

The  number  of  amperes  giving  full  scale  deflection  is  also  stamped 
on  the  shunt.  It  should  agree  with  the  scale  of  the  meter. 

Instruments  of  moderate  range,  say  up  to  75  amp.  in  one  type, 
may  be  had  with  the  shunt  built  in,  concealed  within  the  case. 
The  binding  posts  are  then  of  massive  brass,  with  good  sized  holes 
for  attaching  wires. 

Aside  from  avoiding  rough  treatment,  or  connecting  it  to  carry 
a  greater  current  than  it  is  built  for,  the  chief  precaution  in  using 
an  ammeter  is  to  connect  it  as  shown  in  Fig.  89,  p.  109,  and  not  as  in 
Fig.  90,  which  connection  would  cause  its  instant  destruction. 
That  is,  the  circuit  is  interrupted  at  some  point  and  the  shunt  (or 
the  meter  as  a  whole  if  it  is  self-contained)  is  inserted.  If  not  a 
self-contained  instrument,  the  millivoltmeter  should  then  be  con- 
nected to  the  terminals  of  the  shunt  after  the  latter  has  been 
securely  connected  in  the  circuit. 

Voltmeters. — The  type  of  movement  used  in  ammeters  is  also 
used  in  voltmeters,  but  the  latter  are  connected  to  the  circuit  in  a 
different  way,  which  involves  certain  differences  between  the 
instruments. 

In  Fig.  90,  A  and  B  represent  two  wires  connected  to  the  ter- 
minals of  a  battery.  It  is  desired  to  measure  the  difference  of 
potential,  in  volts,  between  them,  if  is  a  meter  like  that  of  Fig. 
88  and  R  is  a  wire  of  such  great  length  and  small  diameter  that 
its  resistance  is  sufficient  to  keep  the  current  sent  through  the 
instrument  within  proper  limits.  In  one  very  well-known  make 
this  resistance  is  around  15,000  ohms  for  a  meter  reading  up  to 
150  volts. 

The  current  flowing  through  the  instrument,  by  Ohm's  law,  is 
equal  to  the  volts  between  A  and  B  divided  by  the  resistance  of 
R  plus  M.  Any  change  in  the  voltage  will  cause  an  exactly  pro- 
portional change  in  the  current  in  the  meter.  Therefore  it  is  pos- 


112 


RADIO    COMMUNICATION. 


sible  to  graduate  the  scale  directly  in  volts.  As  a  matter  of  fact, 
for  ordinary  voltages,  R  is  usually  wound  on  thin  mica  cards  which 
occupy  little  space  and  are  fastened  permanently  inside  the  case 
of  the  instrument,  out  of  the  way  of  the  user.  He  has  merely  to 
connect  one  binding  post  of  the  meter  to  each  of  the  two  points 
in  question.  The  pointer  indicates,  on  the  scale,  the  voltage 
between  them.  The  main  precautions  to  be  taken  in  using  a 
voltmeter  are  (1)  never  to  connect  it  between  points  of  higher 


FiQ.90 


L_ 

F           5 

Principle  of   Voltmeter  Connectior 


Inclined  Coil  Jy^e.   Meter 


Meter 


voltage  than  the  scale  will  indicate,  even  for  an  instant,  and  (2) 
not  to  shake  or  otherwise  roughly  handle  it. 

The  resistance  of  a  voltmeter  may  be  made  sufficiently  low, 
without  introducing  serious  sources  of  inaccuracy,  to  permit  of  its 
being  used  to  measure  small  fractions  of  one  volt,  in  fact  one  stand- 
ard form  is  made  to  give  full  scale  deflection  on  0.02  volt.  Such 
instruments  are  graduated  in  millivolts  and  are  called  "milli- 
voltmeters."  Even  when  it  is  used  as  in  Fig.  89,  p.  109,  to  measure 
current,  there  are  reasons  why  the  instrument  should  have  some 
resistance  besides  that  of  the  copper  wire  in  the  coil.  This  accounts 
for  the  statement,  made  in  connection  with  that  figure,  that  M  is 
a  millivoltmeter. 


RADIO   COMMUNICATION.  113 

Ammeters  and  voltmeters  can  readily  be  distinguished,  not  only 
by  the  marking  of  the  scale,  but  by  the  terminals.  Those  of  an 
ammeter  are  large,  and  made  to  receive  fairly  thick  wire;  those  of 
a  voltmeter  are  smaller,  having  insulating  caps;  the  screw  threads 
are  fine,  and  it  is  evident  that  they  are  made  to  receive  only  thin 
wires,  as  is  to  be  expected  because  a  voltmeter  takes  a  very  small 
current,  usually  less  than  0.01  amp. 

Other  Types  of  Meters. — For  low  frequency  a.c.  measurements, 
instruments  with  a  permanent  magnet  cannot  be  used,  and  the 
thermal  type  has  not  had  as  wide  application  as  those  types  which 
make  use  of  the  magnetic  effect  of  the  current  on  a  piece  of  soft  iron. 

Fig.  91  illustrates  the  principle  of  one  soft  iron  type.  Cur- 
rent flowing  around  the  coil  C  magnetizes  the  thin  iron  strip  F, 
which  is  fixed  in  position  by  a  stationary  support.  In  the  same 
way  it  magnetizes  the  other  strip  M,  which  is  movable,  being 
supported  from  the  same  shaft  that  carries  the  pointer  P.  The  tops 
of  both  strips  are  at  any  instant  of  the  same  polarity,  and  the  bot- 
tom edges  of  both  are  of  the  opposite  polarity  to  this  (but  of  the 
same  polarity  to  each  other).  They  therefore  repel  each  other; 
the  strip  M  moves  to  the  right,  and  the  pointer  turns  with  it.  The 
motion  is  opposed  by  spiral  springs,  as  in  Fig.  87. 

If  an  instrument  of  this  type  is  to  be  used  as  an  ammeter,  the 
coil  is  made  of  a  few  turns  of  large  wire;  if  it  is  to  be  a  voltmeter, 
many  turns  of  fine  wire  are  used  and  a  resistance  R  is  placed  in 
series  with  the  coil,  inside  of  the  case,  as  in  Fig.  90. 

It  will  be  seen  that  such  an  instrument  will  respond  to  alter- 
nating currents,  for  when  the  current  reverses  the  magnetization 
of  both  of  the  iron  vanes  reverses  at  the  same  time,  so  they  con- 
tinue to  repel  each  other. 

Another  way  of  utilizing  the  magnetic  effect  is  shown  in  Fig.  92. 
The  coil  is  inclined,  and  a  little  iron  vane,  also  inclined,  is  carried 
on  the  pointer  spindle.  When  the  pointer  is  held  in  the  position 
Pt  by  the  controlling  spring,  the  vane  does  not  point  in  the  direc- 
tion of  the  axis  of  the  coil.  Current  sets  up  a  field  and  magnetizes 
the  vane  which  then  tends  to  set  itself  along  the  axis  of  the  coil, 
turning  the  spindle  in  doing  so,  and  moving  the  pointer  against 
the  force  of  the  spring  to  some  position  P2.  The  difference  be- 
tween ammeters  and  voltmeters  of  this  type  is  the  same  as  in  the 
preceding  form. 

97340°— 19 8 


114 


RADIO    COMMUNICATION. 


Telephone  Receiver. — The  magnetic  effect  of  the  current  is  utilized 
in  a  somewhat  different  way  in  the  telephone  receiver.  Fig.  93 
shows,  in  diagram,  the  working  parts  of  a  "watch-case"  receiver  of 
the  kind  used  in  radio  head  sets.  In  the  plan  (6),  MX  is  a  perma- 
nent magnet,  shaped  like  the  letter  C,  to  which  are  attached  the 
soft  iron  strips  terminating  in  the  pole  pieces  JVand  S.  This  magnet  is 
held  in  the  bottom  of  a  circular  metallic  cup,  not  shown  in  (6.)  The 
pole  pieces  project  upward  in  the  center  of  the  cup  as  shown  in  the 
upper  figure  (a) .  A  coil  of  insulated  wire  is  wound  around  each  pole 
piece.  In  high  grade  instruments  the  wire  is  very  fine  and  the  two 


coils  contain  some  thousands  of  turns — around  10,000,  roughly. 
Above  the  pole  pieces,  and  close  to  them,  is  a  thin  circular  disk  D  of 
sheet  iron,  called  the  " diaphragm."  The  diaphragm  of  a  receiver 
can  be  seen  through  the  hole  in  the  center  of  the  hard  rubber  ear- 
piece. 

When  current  flows  around  the  coils  in  one  direction,  it  increases 
the  pull  on  the  diaphragm  due  to  the  permanent  magnet.  If  it  is 
weakened  or  if  it  flows  in  the  opposite  direction  the  attraction  is 
lessened.  A  telephone  current  consists  of  pulsations  in  a  steady 
current,  or,  more  rarely,  of  rapid  reversals  of  direction. 


CHAPTER  2. 

DYNAMO-ELECTRIC  MACHINERY. 

61.  Generators  and  Motors. — In  the  preceding  chapter  some  laws 
of  electric  and  magnetic  circuits  are  discussed,  and  attention  is 
directed  to  the  relations  between  electric  currents  and  magnetic 
fields.     In  the  present  chapter  certain  practical  applications  will 
be  described,  in  which  use  is  made  of  all  those  laws,  but  which  are 
based  particularly  on  three  experimental  facts;  namely,  that — 

1.  When  a  conductor  is  moved  across  a  magnetic  field,  an  emf.  is. 
induced  in  the  conductor. 

2.  When  a  current  flows  in  a  conductor  in  a  magnetic  field,  a  cross- 
push  is  exerted  on  the  conductor. 

3.  When  a  current  is  sent  around  an  iron  core,  the  core  is  magnet- 
ized. 

The  forces  involved  are  not  necessarily  small,  as  is  sometimes 
imagined,  but  may  run  into  hundreds  or  even  thousands  of  kilograms. 
Such  forces  can  be  used  for  power  applications  on  a  large  scale,  by 
means  of  machinery,  called  " dynamo-electric  "  or,  for  short,  " elec- 
trical "  machinery. 

Electric  machines  are  used  for  conversion  of  power  from  mechan- 
ical to  electrical  form,  or  vice  versa.  If  driven  by  some  sort  of 
prime  mover  like  a  steam  engine,  gas  engine,  or  water  wheel,  they 
convert  mechanical  power  into  electrical  power  and  are  called 
"generators."  If  supplied  with  current  and  used  to  drive  machin- 
ery, vehicles,  or  other  devices,  thus  converting  electrical  power 
into  mechanical  power,  they  are  called  "motors." 

While  there  are  various  types  of  motors  and  various  types  of 
generators,  the  difference  is  more  in  the  use  than  in  the  construc- 
tion or  appearance;  in  fact  the  difference  between  most  motors  and 
the  corresponding  kinds  of  generators  is  so  slight  that  the  same 
machine  can  be  used  for  both  purposes  with  no  changes,  or  only 
minor  ones.  Electric  machines  may  be  built  for  either  direct  or 
alternating  current. 

A.  The  Alternator. 

62.  Production  of  Emf.  by  Revolving  Field. — It  was  pointed  out 
in  Chapter  1,  Section  45,  that  the  motion  of  a  conductor  across  a, 
magnetic  field  causes  an  electromotive  force  in  the  conductor.    This 

115 


116 


RADIO    COMMUNICATION. 


is  true  whether  it  is  the  conductor  or  the  magnetic  field  that  actually 
moves;  the  essential  thing  is  that  there  shall  be  relative  motion  of 
one  with  respect  to  the  other. 

One  way  in  which  such  relative  motion  may  be  secured  is  illus- 
trated by  Fig.  94.     Suppose  the  magnet  NS  is  made  to  rotate  con- 


FlQ.94 

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tinuously  in  a  vertical  plane  about  the  axis  mn.  The  loop  of  wire 
ab  is  stationary.  Its  ends  are  connected  to  some  external  part  of  the 
circuit,  X .  As  the  field  from  the  N  pole  sweeps  across  a,  an  electro- 
motive force  is  induced  in  it  to  the  right  and  at  the  same  time  an 
electromotive  force  is  induced  to  the  left  in  b  by  the  passing  of  the  S 


RADIO  COMMUNICATION.  117 

pole.     Thus  the  emf .  produced  tends  to  send  a  current  in  a  clockwise 
direction  around  the  loop  ab,  as  indicated  by  the  arrows. 

When  the  magnet  has  made  half  a  revolution  the  poles  have  ex- 
changed places  with  respect  to  a  and  b  and  the  electromotive  forces 
are  counter-clockwise  around  ab.  As  the  magnet  continues  to  be 
rotated,  there  are  thus  two  pulses  of  electromotive  force  (and  of 
current  if  the  circuit  is  closed)  in  opposite  directions  for  each  revo- 
lution of  the  magnet.  The  device  described  constitutes  a  simple 
"alternating  current  generator"  or  "alternator." 

63.  Direction  of  Emf. — The  direction  of  the  electromotive  force, 
induced  in  the  conductor  can  be  determined  by  the  "right-hand 
rule.','     This  rule  as  generally  stated  assumes  that  the  magnetic  field 
is  stationary  and  that  the  conductor  moves  across  it.     The  extended 
thumb,  forefinger  and  middle  finger  of  the  right  hand  give  respec- 
tively the  directions  of  motion  of  the  conductor,  of  magnetic  flux, 
and  of  the  electromotive  force  induced. 

If  the  magnetic  field  is  moving,  and  the  conductor  stationary, 
the  rule  is  readily  applied  by  recalling  that  the  relative  motion  is 
the  essential  thing.  Thus  in  Fig.  94  the  effect  of  having  the  north 
pole  move  toward  the  reader,  passing  conductor  a,  is  the  same  as  if 
the  conductor  were  to  move  away  from  the  reader,  passing  pole  N. 

64.  Emf.  Curve. — If    the  electromotive  force  is  called  positive 
when  to  the  right  in  a,  and  negative  when  to  the  left,  the  changes  in 
it  may  be  shown  by  a  curve  like  Fig.  95.     Successive  moments 
of  time  are  taken  along  the  horizontal  axis,  and  the  corresponding 
electromotive  forces  are  shown  by  the  height  of  the  vertical  ordinates. 
When  the  north  pole  is  in  position  1,  Fig.  94,  no  emf.  is  induced. 
This  is  shown  by  the  point  marked  1,  Fig.  95.     A  short  time  after- 
ward, in  position  2,  Fig.  94,  a  certain  maximum  emf.  is  induced, 
shown  by  point  2,  on  the  curve.     When  the  pole  has  moved  to  posi- 
tion 3  the  electromotive  force  has  decreased  to  zero,  and  in  position  4 
it  has  reached  a  negative  maximum.     It  then  decreases  again  to 
zero  and  the  whole  series  is  repeated. 

A  curve  like  the  one  in  Fig.  95  is  often  called  an  electromotive 
force  curve  or  wave. 

The  emf.  curves  generated  by  commercial  alternators  have  a 
variety  of  shapes,  but  ordinarily  they  are  not  very  different  from 
sine  curves,  and  for  reasons  given  in  Chapter  1  are  usually  treated  as 
such. 

65.  Cycle,  Period,   Frequency. — A  regularly  recurring  series  of 
values  of  electromotive  force,  from  any  point  in  the  series  to  the  cor- 


118  RADIO    COMMUNICATION. 

responding  point  in  the  next  series,  is  called  a  "cycle. ' '  The  portion 
of  the  curve  in  Fig.  95  from  3  to  7  represents  a  cycle;  similarly, 
the  portion  from  2  to  6.  The  time  required  for  one  cycle  is  the 
"period."  The  number  of  cycles  per  second  is  called  the  "fre- 
quency." 

In  American  commercial  practice,  60  and  25  cycles  per  second 
are  the  most  common  frequencies  for  alternating  current  circuits. 
The  corresponding  periods  are  -fa  and  -^  of  a  second.  Other  fre- 
quencies, for  example  50  cycles,  are  used  in  Europe.  For  certain 
purposes  in  radio  telegraphy,  500-cycle  generators  are  used.  Quite 
recently,  special  machines  have  been  developed  for  generating 
frequencies  as  high  as  100,000  cycles  per  second,  to  be  applied 
directly  to  the  radio  circuits.  This  frequency  corresponds  of  a  radio 
wave  length  of  3000  meters.1 

66.  Multipolar   Magnets. — To  produce  a  frequency  of  60  cycles 
per  second  by  the  use  of  a  single  magnet  with  two  poles  requires  a 
speed  of  rotation  of  60  revolutions  per  second.     Such  a  speed  is  not 
practicable  for  large  machines.     To  get  500  cycles  would  require 
500  r.p.s.,  or  30,000  r.p.m.  (revolutions  per  minute).     By  arranging 
a  number  of  similar  north  and  south  poles  alternately,  as  in  Fig.  96, 
and  providing  corresponding  conductors,  a  lower  speed  of  rotation 
may  be  used.     As  in  Fig.  94,  the  magnet  is  supposed  to  be  made  to 
rotate,  while  the  conductors  a,  b,  c,  d,  e,/ remain  stationary. 

When  the  upper  north  pole  is  coming  toward  the  reader,  electro- 
motive forces  will  be  induced  in  the  several  conductors  in  the  direc- 
tion of  the  arrows.  The  conductors  are  all  connected  in  series, 
except  between  /  and  a,  where  connection  is  made  to  an  external 
part  of  the  circuit,  X.  All  are  in  the  same  relative  position  to  the 
several  magnetic  poles;  their  electromotive  forces  are  equal,  and  in 
the  case  shown,  the  total  is  six  times  as  great  as  the  electromotive 
force  in  any  one  conductor. 

For  every  revolution  of  the  magnet,  each  conductor  is  passed  three 
times  by  an  N  and  three  times  by  an  S  pole.  Each  pair  of  poles  gives 
rise  to  a  cycle,  so  for  each  revolution  there  are  three  cycles  of  emf. 
in  the  conductors.  Thus,  for  a  given  speed,  the  frequency  is  three 
times  as  high  as  it  would  be  if  there  were  but  one  pair  of  poles. 

67.  Field  and  Armature.— The  magnets  (NS,  in  Fig.  96,  p.  116) 
which  produce  the  magnetic  field  of  an  alternator  are  called  the  ' '  field 
magnets. "     If  there  is  but  one  north  and  one  south  pole,  the  machine 

i  Wave  length  explained  in -Sec.  125. 


RADIO  COMMUNICATION. 


119 


is  said  to  be  "  bipolar ; "  if  there  are  several  pairs  of  poles  the  machine 
is  "multipolar." 

The  conductors  in  which  the  electromotive  forces  are  induced 
constitute  the  "armature  winding."  The  winding  is  supported, 
usually  by  being  imbedded  in  slots,  well  insulated,  on  an  iron  or 
steel  core  called  the  "armature  core."  Winding  and  core  together 


FIG.  97. — Windings  partially  assembled  in  a  25-cycle  synchronous  motor. 

constitute  the  "armature,"  though  this  term  is  also  used,  loosely, 
when  the  armature  winding  alone  is  meant. 

68.  Coil-Wound  Armature. — The  electromotive  force  developed 
in  one  conductor  of  an  ordinary  generator  is  only  a  volt  or  two,  not 
enough  for  practical  use.  Armature  windings,  therefore,  consist  of 
a  large  number  of  conductors,  usually  combined  into  coils  (see  Fig. 
97)  of  several  turns  each,  which  are  pushed  into  slots  in  the  face  of 


120 


RADIO    COMMUNICATION. 


the  armature  core  and  then  connected  by  soldering.  The  joints 
have  to  be  carefully  covered  with  tape  or  other  insulating  material. 

The  coils  are  made  of  copper  wire  covered  with  insulation  (usually 
cotton")  wound  to  the  proper  shape  on  a  form,  wrapped  with  tape, 
and  finally  covered  or  impregnated  with  an  insulating  compound. 
The  core  slots  are  often  lined  with  heavy  paper  of  fiber.  After  being 
placed  on  the  core,  the  coils  are  held  by  wedges  of  fiber  or  wood 
driven  into  the  tops  of  the  slots. 

The  core  is  built  up  of  thin  flat  sheets  of  soft  iron  or  steel,  ring- 
shaped,  with  teeth  on  the  inner  edge.  See  Fig.  98.  Enough  sheets 


FIG.  98.— Laminations  partly  assembled,  making  up  the  armature  core  of  a  skeleton 
frame  alternator. 

are  stacked  up  to  make  a  cylinder  of  the  length  desired.  Occa- 
sionally a  separator  is  included  to  provide  air  ducts  through  the 
core  for  ventilation.  The  three  dark  rings  around  the  core  in  Fig. 
97  show  where  the  ducts  are.  The  teeth  are  carefully  lined  up,  and 
the  spaces  between  them  become  the  troughs  or  slots  for  the  windings. 
How  the  emf.  increases  and  decreases  in  such  a  winding  can  be 
studied  from  Fig.  99.  Here  the  coils  are  drawn  as  if  the  armature 
were  unrolled  and  opened  out  flat.  The  magnet  poles  are  supposed 
at  the  given  instant  to  be  over  the  rectangles  marked  N  and  S.  Each 


RADIO  COMMUNICATION. 


121 


of  the  numbered  lines  in  the  figure  may  represent  either  a  single 
conductor  or  one  side  of  a  coil.  Only  a  portion  of  the  armature 
winding  is  represented . 

Imagine  the  poles  in  Fig.  99  to  be  moving  toward  the  right,  the 
conductors  1,  2,  3,  etc. ,  remaining  stationary.  Starting  at  the  instant 
when  a  north  pole  is  just  approaching  conductor  1,  and  a  south  pole 
conductor  5,  electromotive  forces  will  be  induced  in  the  directions 
shown  by  the  arrows.  As  conductors  2  and  6,  3  and  7,  etc.,  are 
reached  additional  electromotive  forces  are  induced.  The  maxi- 
mum comes  when  the  N  pole  covers  1,  2,  3  and  4,  and  the  £  pole 
covers  5,  6,  7  and  8.  After  that  the  resultant  electromotive  force 
begins  to  decrease,  falling  to  zero  and  then  beginning  to  increase  in  the 
opposite  direction.  In  this  manner  an  alternating  emf.  is  gotten 
in  which  the  changes  occur  gradually  as  conductors  get  into  or  out 


f  ia. 


slab  8 


To  show  Add  ition  of  emf.  In 
3ucces9i'v«   coils 


\ 


of  the  magnetic  field  one  by  one,  or  at  least  coil  by  coil.  In  addition 
the  edges  of  the  poles  are  usually  tapered  off  ("chamfered  ")  to  make 
the  changes  still  smoother. 

69.  Concentrated  and  Distributed  Windings. — Sometimes  all  the 
turns  for  one  pair  of  poles  are  combined  into  one  coil,  which  is  put 
into  a  single  pair  of  large  slots,  one  for  each  pole.     Such  a  winding 
is  a  "concentrated"  winding.     (See  Fig.  103.)     When  the  portion 
of  the  core  under  each  pole  face  contains  a  number  of  slots  in  which 
the  coils  are  placed,  the  winding  is  "distributed."     (See  Figs.  97, 
99,  100.) 

70.  Magnetic  Circuit. — It  is  important  to  get  an  understanding  of 
the  magnetic  path  in  an  electric  machine.     Various  shaoes  are 


122 


RADIO   COMMUNICATION. 


2o 


FIG.  101-A-B  (C  and  D  on  opposite  page).— Alternating  current  generator,  150 
ICVA.,  900-R.P.M.,  60-cycle.    Dismantled  parts  listed  below. 


1.  Stator  frame. 

2.  Complete  rotor. 

3.  Shields. 

4.  Journal  boxes. 

5.  Oil  rings. 

6.  Stator  winding. 

7.  Stator  leads. 

8.  Cable  tips  for  leads. 


9.  Oil  gauge. 

10.  Oil  hole  cover. 

11.  Shaft. 

12.  Pole  shoe. 

13.  Collector  ring. 

14.  Field  coil. 

15.  Cap  screws  for  holding 

shields  to  frame. 


16.  Journal  box  set  screw. 

17.  Twin  unit    brush 

holder,  with  brushes. 

18.  Dust  cap. 

19.  Dust  washer. 

20.  Rotor  leads. 

21.  Rotor  lead  cable  tips. 

22.  Brush  stud. 


RADIO   COMMUNICATION. 


123 


possible,  but  an  understanding  of  one  makes  all  others  easy.  Fig. 
100  is  a  diagram  indicating  the  parts  of  a  typical  magnetic  circuit, 
with  their  names.  It  is  not  intended  to  show  details  of  mechan- 
ical construction.  The  fine  lines  in  the  upper  part  of  the  figure 
show  the  path  of  the  magnetic  flux  for  one  pair  of  poles.  The  paths 
for  the  other  poles  are  similar.  The  armature  conductors  are  placed 
in  the  slots  ss. 


124 


RADIO    COMMUNICATION. 


71.  Field  Excitation. — Thus  far  nothing  has  been  said  as  to  how 
the  magnetic  field  is  produced.  While  permanent  magnets  might 
be  used,  they  are  not  satisfactory  for  practical  purposes,  except  in 
the  very  little  machines  called  "magnetos."  Electromagnets  are 
therefore  used.  The  poles  are  fitted  with  coils  or  spools  of  wire, 
usually  of  a  large  number  of  turns,  through  which  direct  current  is 
sent  from  some  external  source. 

The  coils  are  connected  to  a  pair  of  metallic  rings,  called  "slip- 
rings  "  or  collector  rings,  which  are  in  contact  with  conducting  strips, 
called  "brushes,"  connected  to  the  source  of  current.  As  the  entire 
field  structure  rotates,  current  is  brought  to  the  coils  through  the 
sliding  contacts  of  the  stationary  brushes  with  the  revolving  slip  rings. 

The  source  of  direct  current  is  usually  a  separate  small  direct 
current  generator,  which  when  used  for  this  purpose  is  called  an 


R      * 


Production     df    Alte-m^Tin^     etrif.   by    revolving    coil 
l2>   -  Field    mA&net  RR  -Collector   rin^a 


''exciter."  If  used  for  one  alternator  alone  its  output  will  range 
from  1  to  3  per  cent  of  the  rating  of  the  alternator.  When  the  alter- 
nator is  very  small,  like  those  used  in  the  Signal  Corps  portable 
radio  sets,  the  exciter  is  larger,  by  comparison. 

72.  Stator  and  Rotor. — When  it  is  desired  to  refer  to  the  station- 
ary and  rotating  members  of  a  dynamo-electric  machine  without 
regard  to  their  functions  the  former  is  called  the  "stator"  and  the 
latter  the  ' '  rotor. ' ' 

73.  Arrangement  of  Parts. — A  good  idea  of  the  parts  of  a  revolving- 
field  alternator  is  obtainable  from  the  pictures  in  Fig.  101,  which 
show  a  complete  machine,  as  well  as  views  of  the  most  important 
parts.    The  general  view  shows  how  the  parts  fit  together. 


RADIO   COMMUNICATION.  125 

Through  the  holes  in  the  ventilated  iron  frame  of  the  stator  the 
outside  of  the  core  is  visible.  On  the  inside  of  the  core  the  lami- 
nations can  be  dimly  seen.  The  two  dark  rings  which  seem  to  divide 
the  core  into  thirds  are  ventilating  ducts.  Where  the  windings  lie 
in  the  slots  they  are  concealed  by  the  wedges,  but  the  ends  of  the 
coils  are  in  plain  view.  Note  that  the  coil  ends  are  given  a  twist 
to  make  a  neat  construction.  The  four  terminals  at  the  left  of  the 
stator  indicate  a  two-phase  machine  (Section  76). 

The  right  hand  end  shield  shows  one  brush  holder  in  place,  to  the 
left  of  the  bearing;  the  little  hole  to  the  right  of  the  bearing  is  for 
the  stud  on  which  the  other  brush  holder  (lying  in  front)  is  to  be 
mounted. 

The  brushes  of  one  set  slide  on  one  collector  ring,  and  those  of  the 
other  set  on  the  other  ring.  Two  brushes  are  used  in  each  set,  in 
this  particular  machine,  in  order  to  have  a  large  and  reliable  contact. 
The  ends  of  the  cables  leading  to  the  brushes  are  in  view  on  the  right 
of  the  complete  generator. 

On  the  rotor  the  pole  shoes  are  noticeable,  held  on  by  six  screws. 
One  of  the  connections  between  field  coils  is  seen  between  the  upper 
pole  shoe  and  the  one  just  in  front  of  it,  near  the  center  of  the  shoe. 
The  massive  ring  to  which  the  pole  cores  are  attached  is  also  visible. 
There  are  two  collector  rings  close  together,  though  it  is  a  little  diffi- 
cult to  distinguish  them  in  the  picture. 

74.  Other  Forms  of  Alternator. — Thus  far  we  have  considered 
alternators  of  which  the  field  magnets  revolve,  while  the  armature 
is  stationary.  That  is  the  construction  generally  used  on  large  ma- 
chines, one  reason  being  that  it  makes  the  armature  easier  to 
insulate.  But  it  is  also  possible  to  have  the  field  magnets  stationary 
while  the  armature  is  made  to  revolve.  Small  machines  are  often 
built  this  way.  The  principle  is  shown  in  Fig.  102. 

The  magnetic  field  occupies  the  space  between  the  poles  N  and  S 
of  the  stationary  field  magnet.  The  turn  of  wire  ab  is  made  to 
revolve  about  a  horizontal  axis  in  this  magnetic  field.  When  a  is 
passing  under  the  N  pole,  coming  toward  the  reader,  the  electro- 
motive force  in  it  is  to  the  right,  and  that  in  b  which  is  cutting 
through  the  same  field  (the  direction  of  the  magnetic  flux  is  from 
the  N  pole  into  the  S  pole),  but  moving  away  from  the  reader  is  to 
the  left.  Current  will  therefore  flow  in  the  turn  of  wire,  and  by 
way  of  the  collector  rings  and  brushes  in  the  external  circuit,  as 
shown  by  the  arrows. 


126 


RADIO    COMMUNICATION. 


When  the  loop  has  made  half  a  revolution,  a  is  passing  in  front  of 
the  S  pole  and  the  electromotive  force  in  a  is  toward  the  left.  In  b 
it  is  toward  the  right.  In  the  external  portion,  X,  of  the  circuit  the 
flow  of  current  will  then  be  opposite  in  direction  to  the  arrows. 


FIG.  103.— Circuit  diagram  of  revolving  armature  alternator.  A,  armature;  F, 
frame;  P,  poles;  R,  collector  rings;  B,  brushes;  FF,  terminals  of  field  circuit; 
XX,  leads  to  external  circuit. 

The  continued  rotation  of  the  loop  thus  causes  an  alternating  cur- 
rent to  flow  in  the  circuit. 

The  simple  bipolar  magnet  of  Fig.  102  may  be  replaced  by  a 
multipolar  electromagnet  consisting  of  a  massive  cylindrical  frame 
called  the  ' '  yoke, ' '  from  which  poles  project  radially  inward.  Direct 
current  is  sent  through  coils  or  spools  on  the  magnet  poles.  The 
same  kinds  of  windings  are  used  for  the  revolving  armature  as  are 


RADIO   COMMUNICATION. 


127 


used  for  the  stationary  kind;  the  only  difference  is  that  they  are 
put  on  the  outside  instead  of  on  the  inner  face  of  the  core. 

A  machine  in  which  the  field  magnets  are  stationary,  while  the 
conductors,  in  which  the  electromotive  force  is  induced  are  rotated, 
is  said  to  be  of  the  "revolving  armature"  type.  A  diagram  of  such 
a  machine,  used  in  one  form  of  radio  pack  set,  is  given  in  Fig.  103. l 
The  armature  winding  in  this  case  is  of  the  concentrated  type.  A 
picture  of  a  generator  very  much  like  it  appears  in  Fig.  122. 

It  has  previously  been  shown  that,  when  the  field  is  made  to 
revolve,  slip-rings  have  to  be  used  in  the  field  circuit.  Similarly, 
when  the  armature  is  the  part  that  revolves,  there  must  be  slip- 


tn_ 


LULL? 


mf  by 


Producti'on    of    A,lfernd 
movm^     iron    Inductor* 
•4.3-  Poles   of  .stAtion<irv   electromagnet 
C|Cz- Cores  of  jiUtionAry   «srmtiture 
^A   -  Coils    in  Which  alfernatini  «mf  li  induced 
1 1  —  Movioi   rrvis^ea  of  iron  ("ir»ciuctor~.3"J 

revolved  ^beut*  ax l«    mn. 


Production   of   C 


rings  in  the  armature  circuit  to  provide  connection  with  the  external 
portion.  Such  rings  are  shown  at  R  R  in  Fig.  102. 

Inductor  Alternator. — Another  type  of  alternator  is  of  especial 
interest  in  connection  with  radio  telegraphy.  It  is  called  the  ''in- 
ductor alternator,"  and  is  used  particularly  for  the  generation  of 
continuous  high  frequency  currents,  say  around  100,000  cycles  per 
second,  but  is  also  used  for  lower  frequencies. 

The  principle  on  which  such  machines  operate  is  illustrated  in 
elementary  form  in  Fig.  104.  The  field  magnet  and  the  armature 

1  The  little  machine  to  which  this  diagram  applies  has  18  field  poles  and  18  arma- 
ture teeth,  runs  3333  r.p.m.,  and  generates  current  of  500  cycles  frequency.  It  is 
designed  for  an  output  of  250  volt-amperes,  to  be  used  in  a  field  radio  pack  set.  The 
windings  are  shown  only  hi  diagram;  actually  the  field  coils  average  250  turns  each; 
the  armature  coils  19  turns  each.  The  sketch  is  practically  to  scale,  except  the  col- 
lector rings,  which  are  drawn  smaller  so  as  not  to  conceal  the  armature.  The  whole 
diameter  across  the  frame  is  about  15  cm.  (6  in.). 


128  RADIO    COMMUNICATION. 

are  both  stationary.  A  considerable  gap  separates  the  armature 
core  from  the  faces  of  the  field  poles.  In  this  gap  are  masses  of  iron, 
/,  free  to  revolve  in  a  plane  perpendicular  to  the  plane  of  the  paper 
about  the  axis  mn.  These  masses  of  iron  are  called  ' '  inductors. ' '  Im- 
agine them  made  to  revolve  by  an  external  force.  When  the  induc- 
tors are  in  the  position  shown,  between  N  and  C1?  and  S  and  C2  there 
is  a  certain  magnetic  flux,  due  to  the  d.  c.  excitation.  When  the  induc- 
tors are  not  in  that  position  there  are  long  air  gaps  in  the  magnetic 
circuit,  which  have  a  very  much  smaller  permeability  than  the 
iron  inductors.  The  flux  is  consequently  less.  The  increase  and 
decrease  of  magnetic  flux  in  the  coils  A  A  sets  up  an  alternating  emf . , 
because  any  change  in  the  flux  inclosed  by  a  circuit  sets  up  an  emf. 
in  the  circuit  (Sec.  45)  in  the  one  direction  while  the  flux  is  increasing, 
and  in  the  opposite  direction  while  it  is  decreasing. 

In  this  type  of  alternator,  the  passing  of  each  mass  or  inductor 
causes  a  complete  cycle  of  emf.,  whereas  with  alternators  of  either 
the  revolving  field  or  the  revolving  armature  type  it  requires  the 
passage  of  two  poles  to  cause  a  cycle. 

75.  Polyphase  Alternators. — Suppose  that  in  Fig.  94,  p.  116,  another 
loop  similar  to  aft,  but  entirely  independent  of  it,  were  placed  at 
right  angles  to  aft,  as  shown  at  cd  in  Fig.  105.  The  rotation  of  NS 
would  induce  in  the  second  loop  an  alternating  emf.  identical  with 
that  in  the  first,  having  the  same  frequency  and  the  same  series  of 
values.  The  sole  difference  would  be  that  they  would  reach  corre- 
sponding points  in  the  cycle  at  different  instants  of  time,  for  at  the 
moment  when  the  poles  were  in  line  with  the  conductors  of  one 
loop  and  it  was  having  maximum  emf.  induced,  the  other  loop 
would  have  none. 

Suppose  the  emf.  wave  of  the  first  winding  is  given  by  curve  I, 
Fig.  106.  Then  curve  II  will  represent  the  emf.  of  the  other 
winding.  The  two  curves  are  first  shown  separately  and  then 
combined  into  one  diagram.  They  are  alike  in  shape,  showing 
that  the  two  emfs.  go  through  the  same  series  of  values,  but  II  is 
always  a  quarter  of  a  cycle  behind  I  (see  Sec.  55).  Suppose  the 
distance  0—4  represents  -fa  second.  Then  whatever  happens  in  I, 
at  any  instant,  happens  in  II  just  ^  second  later.  This  is  expressed 
by  saying  that  there  is  a  "  phase  difference "  of  a  quarter  cycle 
between  them,  or  that  the  two  emfs.  differ  in  phase  by  a  quarter  cycle. 

Two  emfs.  which  differ  in  phase  by  a  quarter  of  a  cycle  are  said  to  be 
in  quadrature.  A  generator  giving  such  a  pair  of  emfs.  in  quadrature 
is  called  a  "two-phase"  alternator.  The  two  windings  considered 


RADIO  COMMUNICATION. 


129 


separately  are  called  " phase  windings,"  or,  somewhat  loosely,  the 
"phases."  Either  one  may  be  thought  of  as  phase  I  and  the  other 
as  phase  II. 

It  will  now  be  plain  why  the  pictures  of  Fig.  101,  show  four  termi- 
nals at  the  left.     Two  belong  to  one  phase  and  two  to  the  other. 


Lmf   curves  -for  "Z 
1    Curve -Jor  one    J>hase 
IL  Curve  ^or  other   ^hase 
FlCj.  10T 


Curves  for  tfjf ee - 


Star  or  Y 


Fid. 106 


Three    f>ha«.e   connection* 


There  may  be  more  than  two  phases,  in  fact,  modern  power- 
generators  usually  have  three  phase  windings. 

Definitions. — A  machine  for  a  simple  alternating  current  is  called 
a  "single  phase"  machine.  Generators  used  exclusively  for  radio 
communication  are  generally  single  phase. 

A  machine  for  alternating  current  of  two  or  more  phases  is  called  a 
' ' polyphase  "  machine;  polyphase  generators  are  either  two-phase  or 
97340°— 19 9 


130  RADIO    COMMUNICATION. 

three-phase,  almost  without  exception.  They  are  used  for  power 
purposes. 

Arrangement  of  Windings. — An  idea  of  the  way  the  windings  of  a 
polyphase  generator  are  arranged  may  be  obtained  by  referring  back 
to  Fig.  99.  Suppose  another  winding  to  be  added,  identical  with 
the  one  shown,  "but  occupying  the  spaces  left  vacant  by  the  first 
winding.1  As  the  magnet  poles  move  along,  the  windings  come  into 
play  alternately. 

Notice  that  in  a  single  phase  generator  half  the  surface  of  the 
armature  core  has  to  be  left  vacant.  In  a  polyphase  generator,  on  the 
contrary,  the  windings  may  cover  the  entire  surface  and  usually  do. 

Next,  suppose  the  two-phase  windings  were  each  made  narrower, 
leaving  space  for  a  third  winding  just  as  large  as  each  of  the  first  two. 
We  should  then  have  three  phase  windings,  and  a  given  field  pole 
would  pass  them  one  after  the  other.  Thus  would  be  produced 
three  emfs.  differing  in  phase  by  equal  amounts. 

By  properly  selecting  the  terminals,  the  three  emfs.  would 
follow  one  another  as  represented  in  Fig.  107,  and  it  will  be  seen 
that  now  the  difference  between  them  is  one-third  of  a  cycle.  In 
the  time  of  one  cycle  each  of  the  three  comes  to  a  positive  peak  one 
after  the  other.  The  emf.  curves  are  shown  in  Fig.  107.  The 
emfs.  are  often  spoken  of  as  differing  by  120°. 

It  might  be  expected  that  a  three-phase  machine  would  have  six 
terminals.  As  a  matter  of  fact,  the  phases  are  usually  so  connected 
in  the  machine  that  three  terminals  are  sufficient,  as  illustrated  in 
Fig.  108.  The  three  coils  stand  for  the  three  armature  windings. 
When  joined  as  in  the  upper  sketch,  they  are  said  to  be  connected 
in  "delta"  when  one  end  of  each  coil  is  brought  to  a  common  junc- 
tion as  at  0  in  the  middle  figure  they  are  connected  in  "  Y  "  or  "  star. ' ' 
The  lower  figure  is  the  same  as  the  middle  one,  in  that  terminals 
2,  4,  6  are  all  joined  together  and  1,  3,  5  are  connected  to  the  line- 
wires  J.,  B,  C.  By  changing  the  position  on  the  paper  the  connec- 
tions are  made  to  look  simpler. 

The  scheme  of  connections  is  ordinarily  of  no  interest  to  the 
operator,  except  in  case  of  trouble,  and  cannot  be  determined 
without  a  close  examination.  The  wires  by  which  the  connections 
are  made  are  carefully  wrapped  and  tucked  away  at  the  end  of  the 

1  The  reader  who  has  difficulty  in  imagining  the  second  winding  may  trace,  on 
transparent  paper,  the  winding  shown  and  may  then  slide  the  paper  to  one  side  by 
the  proper  amount. 


RADIO  COMMUNICATION.  131 

armature,  concealed  by  an  overhanging  part  of  the  frame,  or  by  the 
end  shield,  which  has  to  be  taken  off  before  the  connections  can  be 
traced.1 

B.  Alternator  Theory,  Losses  and  Efficiency. 

76.  Equations  for  Frequency  and  Emf.  —  The  frequency  of  the  emf. 
generated  by  an  alternator  of  the  revolving  field  or  revolving  arma- 
ture type  is  given  by  the  equation: 

/=for/=^  (65) 

where  /  =  frequency  in  cycles  per  second. 
p  =number  of  poles. 
n  =revolutions  per  second. 
n/=revolutions  per  minute. 

The  passing  of  each  pair  of  poles,  ^  in  number  gives  rise  to  one 
cycle.  If  there  are  n  revolutions  per  second,  the  number  of  cycles 
per  second  is  therefore  ^  Xn.  The  second  form  of  the  equation  is 

given,  because  the  speed  is  commonly  given  in  revolutions  per 
minute. 

For  example:  What  frequency  will  a  12-pole  alternator  give  when  running  at 
SOOOr.p.m.? 

With  12  poles,  each  revolution  gives  6  cycles.  In  a  minute  there  will  be 
6X5000=30,000  cycles.  In  a  second  there  are  30,000-=-  60=  500  cycles.  The  machine 
gives  500  cycles  per  second.  By  the  second  formula  we  get  the  same  answer 


For  the  inductor  type  the  frequency  is  the  same  as  the  number 
of  inductors  which  pass  a  given  point  per  second.  Thus  40  teeth 
at  25  r.p.s.  give  1000  cycles  per  second.  The  inductors  are  usually 
in  the  form  of  teeth,  somewhat  like  gear  teeth,  that  project  from  the 
revolving  part. 

The  emf  .  generated  in  an  alternator  depends  on  how  much  magnetic 
flux  is  cut  by  the  conductors  per  second.  Increasing  either  the 
magnetic  flux  from  each  pole,  or  the  number  of  poles  that  pass  a. 
given  conductor  in  a  second,  or  the  number  of  conductors  connected 
in  series  (so  that  the  effects  in  them  are  added  together)  increases  the 

1  Discussion  of  this  subject  can  be  found  in  any  textbook  on  alternating  current 
machinery.  See,  for  example,  Timbie  and  Higbie,  First  Course,  pp.  114-128;  Frank- 
lin &  Esty,  Elements  of  Electrical  Engineering,  vol.  2. 


132  KADIO    COMMUNICATION. 

emf .  of  the  machine  in  a  corresponding  way.  This  may  all  be  stated 
in  one  equation. 

E=<j>Nfk  (66) 

where  J£=  effective  volts  (Section  53),  as  shown  by  a  voltmeter. 

9= magnetic  flux  per  pole,  in  maxwells  or  ' '  lines  of  magnetic 

force. " 

AT=  number  of  turns  of  armature  winding  connected  in  series. 
f  =frequency  in  cycles  per  second. 

fc=a  multiplier  that  depends  on  the  arrangement  of  the 
winding  and  certain  mathematical  relations  not  neces- 
sary to  consider  here.1 

77.  Dependence  of  Driving  Power  on  Current. — The  power  con- 
sumed in  an  electrical  circuit  at  any  instant  is  proportional  to  the 
emf.  and  also  to  the  current.  It  is  therefore  proportional  to  their 
product.  If  the  current  is  made  to  flow  by  means  of  a  generator, 
and  if  the  generator  is  driven  by  an  engine  of  some  sort,  the  power 
that  has  to  be  developed  by  the  engine  evidently  depends  upon  the 
power  used  in  the  circuit.  It  is  worth  while  to  trace  the  reason  why 
increased  current  in  a  generator  calls  for  more  power  from  the  engine 
that  drives  it. 

Let  the  simple  loop  in  Fig.  102  be  made  to  rotate  at  constant 
speed  by  any  "prime  mover"  suitably  governed.  This  prime 
mover  may  be  anything  that  will  make  the  loop  go  around— a  man 
turning  a  crank,  a  gasoline  engine,  a  steam  engine,  an  electric 
motor,  etc.  At  the  instant  when  the  loop  is  in  the  plane  of  the 
paper,  and  a  is  coming  toward  the  reader,  an  emf.  is  being  induced 
in  it,  in  the  direction  of  the  arrow.  If  the  circuit  is  closed,  a  current 
flows  in  the  same  direction.  But  it  is  known  (see  Section  43)  that 
when  a  conductor,  carrying  a  current,  is  in  a  magnetic  field,  the  con- 
ductor tends  to  move  across  the  field.  The  force  on  the  conductor  is 
proportional  to  the  strength  of  the  field  and  to  the  current.  The 

1  The  student  who  has  some  previous  knowledge  of  electricity  will  see  that  if  2/ 
poles  pass  a  conductor  per  second,  the  average  flux  cut  per  second  is  2/x<£.  To 
generate  1  volt  requires  passing  108  lines  of  flux  per  second.  Hence  the  average  volts 
per  conductor  are  2/x<£-Hl08.  Each  turn  consists  of  two  conductors  in  series,  so  we 
multiply  by  2.  The  voltmeter  reads  not  average  but  effective  volts.  For  sine 
waves  the  effective  volts  are  1 . 1 1  times  the  average,  so  we  multiply  by  1 . 1 1 .  Collect- 

2v2vl  11      4  44 
ing  all  the  numbers  it  is  seen  that  k  in  the  formula  stands  in  part  for       ^  '    •  °r-jr«  • 

It  also  includes  a  factor,  not  greater  than  1,  depending  on  the  kind  of  winding  used, 
because  if  the  winding  is  distributed,  the  emfs.  in  the  various  turns  do  not  rise  and 
fall  together  (there  is  a  difference  in  phase),  and  this  must  also  be  taken  into  account. 


RADIO  COMMUNICATION.  133 

direction  of  the  force  is  given  by  the  left  hand  rule.1  Applying  the 
left  hand  rule  to  conductor  a,  it  is  seen  that  the  force  on  it  is  away 
from  the  reader,  opposite  to  the  direction  in  which  the  conductor  is 
being  driven,  so  that  the  wire  is  harder  to  push  than  it  would  be  if 
there  were  no  current.  The  greater  the  current  in  the  Conductor, 
the  greater  must  be  the  force  exerted  to  drive  it  around,  and  there- 
fore the  greater  must  be  the  power  developed  by  the  prime  mover 
in  keeping  up  a  given  speed.  The  same  reasoning  applied  to  b  shows 
that  it  acts  with  a  in  opposing  rotation. 

78.  Losses. — Of  the  mechanical  energy  supplied  to  a  generator 
by  its  prime  mover,  not  all  appears  in  electrical  form  in  the  cir- 
cuit. Some  is  unavoidably  transformed  into  heat,  and  thus  lost  for 
practical  purposes.  The  losses,  which  may  be  called  power  losses 
or  energy  losses,  may  be  classified  as — 

1.  Mechanical  losses. 

2.  Copper  losses. 

3.  Core  losses. 

Mechanical  losses  are  those  due  to  friction  in  the  bearings,  friction 
at  the  brush  contacts,  and  friction  between  the  air  and  the  moving 
part  of  the  machine,  commonly  called  windage.  The  latter  is  not 
important  in  low  speed  machines,  but  becomes  prominent  in  the 
case  of  very  high  speed  generators.  Generators  of  the  kind  we  are 
discussing  are  driven  at  nearly  constant  speed,  so  the  mechanical 
losses  do  not  depend  much  on  the  load,  whether  large  or  small. 
They  do  depend  very  greatly  on  the  condition  of  the  bearings  and 
brushes.  Some  points  regarding  the  care  of  machines  in  this  re- 
spect are  given  at  the  end  of  this  chapter,  in  Section  106. 

Copper  losses  are  due  to  the  flow  of  current  against  the  resistance 
of  the  field  and  armature  windings.  They  are  therefore  divided 
into  two  parts,  field  copper  loss  and  armature  copper  loss.  The 
former  is  also  called  "excitation  loss."  Since  the  field  coils  have 
resistance  (usually  high)  some  heat  is  produced  as  the  necessary 
current  for  magnetization  is  made  to  flow  through  them.  Like  all 
heat  losses  due  to  current  in  a  conductor,  the  heating  is  propor- 
tional to  the  square  of  the  current,  being,  in  watts, 

W=I?Rt  (67) 

where  If  is  the  current  in  amperes  in  the  field  coils  and  Rf  is  the 
resistance  of  the  whole  field  circuit. 

i  The  thumb,  forefinger,  and  middle  finger,  all  at  right  angles,  giving  respectively 
the  directions  of  motion,  flux,  and  current. 


134  RADIO    COMMUNICATION. 

To  get  the  same  terminal  voltage  at  the  armature,  when  the  cur- 
rent in  the  latter  is  large,  requires  more  magnetization  than  when 
the  armature  current  is  small.  This  in  turn  requires  more  field 
current,  hence  the  field  copper  loss,  or  excitation  loss,  is  somewhat 
greater  at  large  loads  than  at  small  loads;  that  is,  it  varies  some- 
what with  the  load. 

Like  the  field  loss,  the  armature  copper  loss  is  of  the  I2R  type;  it 
varies  as  the  square  of  the  armature  current,  and  therefore  as  the 
square  of  the  load  on  the  generator.  The  armature  resistance  is 
made  as  small  as  is  expedient.  In  a  large  generator  it  may  be  only 
a  small  fraction  of  1  ohm,  but  the  loss  due  to  the  great  current  gen- 
erated will  nevertheless  be  considerable. 

Core  losses,  or  losses  in  the  magnetic  circuit,  are  of  two  classes,  due 
to  "hysteresis"  and  "eddy  currents."  Hysteresis  losses  are  caused 
by  the  rapid  reversals  of  the  magnetism  of  the  armature  core.  Each 
molecule  of  the  core  may  be  regarded  as  a  tiny  magnet,  and  when 
the  magnetization  of  the  core  is  changed  in  direction,  the  molecules 
have  to  be  pulled  around  against  their  mutual  magnetic  attractions. 
It  takes  energy  to  accomplish  this.  In  an  electric  machine  there  is 
a  double  reversal  during  each  cycle.  This  makes  many  reversals 
per  second  and  requires  considerable  power. 

Eddy  currents  are  little  electric  currents  induced  in  the  iron  sheets 
of  which  the  armature  core  is  made  up.  The  thinner  the  sheets,  the 
smaller  are  the  currents;  in  fact,  it  is  because  of  the  eddy  currents 
that  the  core  has  to  be  laminated. 

Both  hysteresis  and  eddy  currents  produce  heat  in  the  core,  and 
in  producing  heat  they  use  up  power  which  has  to  be  furnished  by 
the  prime  mover.  Therefore  they  are  wasteful,  and  the  designers 
of  electric  machinery  plan  to  keep  them  as  small  as  possible. 

No  specific  statement  can  be  made  regarding  the  magnitudes  of 
the  various  losses  described  in  the  preceding  paragraphs,  because 
they  depend  on  many  factors,  such  as  the  size,  the  operating  speed, 
and  special  features  of  design.  But  in  order  to  give  the  reader  some 
idea,  it  may  be  said  roughly  that  at  full  load,  for  generators  of  the 
usual  types,  the  mechanical  or  frictional  losses  may  range  from  6 
per  cent  for  a  1-kw.  machine,  to  1  per  cent  for  the  1000-kw.  size; 
the  excitation  loss,  from  6  to  1  per  cent;  the  armature  resistance  loss, 
from  4  to  1  per  cent;  and  the  core  loss  from  4  to  2  per  cent. 

It  will  now  be  clear  why  the  allowable  power  output  of  a  generator 
has  a  limit.  Usually  machines  are  heavy  enough  to  give  a  large 
margin  of  strength,  but  they  cannot  well  be  made  large  enough  to 


RADIO  COMMUNICATION.  135 

allow  for  the  heat  produced  by  severe  overloads  long  continued. 
The  increased  current  causes  heat  to  be  produced  more  rapidly,  and 
the  temperature  rises.  High  temperature  is  injurious  to  the  insu- 
lation. For  example,  it  is  found  that  cotton  should  not  be  continu- 
ously heated  as  hot  as  the  boiling  point  of  water.  Cotton  is  the 
usual  insulation  for  the  copper  wires  used  in  machinery.  If  the 
insulation  is  spoiled,  the  current  can  follow  other  paths  than  those 
it  should,  and  the  machine  is  ruined. 

79.  Rating;  Name  Plate  Data. — Practically  all  electrical  appa- 
ratus, whether  for  alternating  or  for  direct  current  generator,  motor, 
or  other  device,  is  designed  for  certain  definite  conditions  of  opera- 
tion. It  is  standard  commercial  practice  to  attach  firmly  to  every 
electrical  machine  before  it  leaves  the  factory,  a  brass  information 
tag  called  a  "name  plate."  This  usually  gives  the  serial  number 
by  which  the  machine  can  be  identified,  tells  the  maker's  name; 
states  whether  the  machine  is  a  generator  or  a  motor;  what  is  the 
maximum  continuous  power  output;  whether  for  direct  or  alternating 
current;  if  alternating,  for  what  frequency  and  how  many  phases;  at 
what  speed  it  is  to  be  operated;  at  what  voltage;  the  maximum  cur- 
rent for  continuous  operation.  Some  of  these  items  are  at  times 
omitted,  but  most  of  them  are  essential.  A  person  who  wishes  to 
become  familiar  with  electrical  machinery  should  form  the  habit  of 
examining  the  name  plate  of  every  machine  to  which  he  has  access, 
and  note  the  differences  in  size,  construction  and  use. 

It  has  been  previously  said  that  electrical  power  is  measured  in 
watts  (or  kilowatts,  ' '  kw. , ' '  when  large) .  In  a  direct  current  circuit, 
watts  are  the  product  of  volts  times  amperes.  With  alternating 
current  something  else  has  to  be  taken  into  account,  and  to  get  the 
average  power  we  must  multiply  the  volts- times-amperes  by  the 
"power  factor."1  We  might  expect  to  find  a.c.  machines  rated  in 
watts  or  kilowatts,  but  if  we  look  at  the  name  plate  of  a  generator 
we  are  likely  to  find  the  letters  "kva."  (kilo volt-amperes).  That 
is,  instead  of  actual  watts  the  permissible  output  is  expressed  as  a 
product  of  amperes  times  volts  divided  by  1000.  The  reason  is 
plain,  if  we  remember  that  the  whole  question  of  what  an  electric 
machine  will  stand  hinges  altogether  on  the  heating. 

1  Power  factor  is,  in  fact,  the  number  by  which  we  must  multiply  volt-amperes 
to  get  true  watts.  (See  Sec.  57.)  It  is  commonly  expressed  in  per  cent.  It  cannot 
be  over  100  per  cent  and  is  usually  less.  It  depends  entirely  on  the  sort  of  circuit 
that  happens  to  be  connected  to  the  generator,  since  this  as  well  as  the  generator 
itself  controls  the  phase  difference  existing  between  volts  and  amperes. 


136  RADIO    COMMUNICATION. 

The  heating  of  the  field  coils  and  armature  core  depends  upon  the 
voltage  generated,  because  that  is  determined  by  the  strength  of 
the  magnetic  field,  which  in  turn  depends  on  the  current  in  the 
field  coils.  The  heating  of  the  armature  conductors  is  determined 
by  the  armature  current;  whether  or  not  that  is  in  phase  with  the 
emf.  makes  no  difference.  The  total  heating,  then,  depends  on  the 
volts  and  the  amperes,  regardless  of  the  power  output  which  may 
be  large  or  small,  depending  on  the  phase  relation  between  the  two. 

80.  Efficiency. — The  ratio  of  the  useful  output  of  a  device  to  its 
input,  is  called  its  "efficiency." 

In  all  kinds  of  machinery  it  is  impossible  to  avoid  some  losses  of 
power,  so  the  output  is  less  than  the  input  and  the  efficiency  is  less 
than  100  per  cent.  It  is  lower  for  small  electrical  machines  than 
for  large  ones,  and  for  a  given  machine  it  varies  with  the  extent  to 
which  the  machine  is  loaded.  Certain  losses  go  on  regardless  of  the 
load;  those  are  the  mechanical  losses,  field  excitation  and  core  losses. 
Others  increase  with  the  load;  the  armature  copper  loss  rapidly, 
some  additional  core  losses  and  a  portion  of  the  excitation  loss  more 
slowly.  When  the  output  is  small,  most  of  the  power  input  is  used 
up  in  the  constant  losses,  and  the  efficiency  is  low.  With  very  large 
outputs,  the  variable  losses  become  excessive,  again  lowering  the 
efficiency.  For  some  intermediate  load,  usually  not  far  from  the 
rated  load  given  on  the  name  plate,  the  efficiency  is  a  maximum. 
At  full  load,  and  for  the  usual  designs,  it  may  range  from  80  per  cent 
for  a  1-kw.  generator  to  95  per  cent  for  a  1000-kw.  generator. 

81.  Regulation. — Electric    generators  are,   with  few  exceptions, 
intended  to  be  operated  at  constant  or  nearly  constant  speed. 
Assuming  that  the  speed  is  constant,  and  that  the  field  excitation  is 
also  constant,  the  generated  voltage  would  likewise  be  constant, 
regardless  of  the  current  output  if  it  were  not  for  certain  disturbing 
influences.     A  generator  operating  under  these  conditions  is  often 
called  a  "constant  potential"  or  "constant  voltage"  machine. 

The  current  output  depends  on  what  is  going  on  in  the  external 
circuit.  In  a  city  it  might  depend  on  the  number  of  lamps  turned 
on.  In  the  case  of  a  generator  supplying  energy  to  a  spark  gap,  it 
would  depend  largely  on  the  adjustment  of  the  gap.  The  term 
"load"  is  commonly  used  in  this  connection.  Sometimes  it  means 
the  devices  themselves,  which  are  connected  to  the  line,  and  some- 
times the  current  taken  by  them.  There  is  generally  no  trouble  in 
knowing  which  is  meant. 


RADIO   COMMUNICATION.  137 

Suppose  we  have  a  certain  voltage  generated  when  the  load  is 
zero  Then  if  the  machine  is  made  to  supply  current  to  a  circuit, 
the  voltage  at  its  terminals  will  in  general  be  lowered,  and  the 
greater  the  current,  the  more  will  the  voltage  be  reduced.  The  term 
by  which  the  behavior  of  a  generator  is  described  in  this  respect  is 
called  the  "regulation."  It  is  found  by  subtracting  the  voltage 
at  full  load  from  the  voltage  at  no  load,  dividing  by  the  full  load 
voltage  and  multiplying  by  100  to  get  the  result  in  per  cent. 

Expressed  as  a  formula — 

/V  —  V\ 
Regulation=(  — ^ — -MX  100  per  cent. 

where  V0= voltage  at  no  load  and 
Ff=voltage  at  lull  load. 

A  small  percentage  regulation  means  that  the  voltage  remains 
quite  steady  when  the  load  is  changed. 

82.  Armature  Impedance  and  Armature  Reaction. — There  are  two 
reasons  why  the  voltage  of  a  generator  is  lower  when  it  is  supplying 
current  than  when  it  is  not  supplying  current,  even  if  the  speed  is 
entirely  steady  and  the  direct  current  flowing  around  the  field 
magnets  is  the  same. 

(a)  The  armature  windings  are  bound  to  have  some  resistance  and 
some  reactance.  It  requires  an  emf.  to  send  current  through  the 
armature,  therefore.  This  emf.,  called  the  armature  impedance 
drop,  has  to  be  subtracted  from  the  emf.  generated  to  get  the  emf. 
left  to  send  current  through  the  external  circuit.  The  greater  the 
current,  the  greater  the  armature  impedance  drop,  and  the  less  the 
emf.  left  for  the  external  circuit. 

(6)  The  armature  winding  and  core  constitute  an  electromagnet. 
When  current  flows  in  the  windings,  the  magnetic  field  caused  by 
it  is  combined  with  the  magnetic  field  due  to  field  strength,  with 
consequent  decrease  in  armature  voltage,  since  the  resultant  mag- 
netic field  is  what  determines  the  generated  emf. 

The  change  in  the  field  flux  by  reason  of  the  current  flowing  in 
the  armature  is  called  "armature  reaction."  Armature  reaction 
occurs  in  direct  current  as  well  as  in  alternating  current  machines, 
and  in  motors  as  well  as  generators.1 

83.  Effect  of  Power  Factor  on  Regulation. — The  reduction  of  ter- 
minal voltage  due  to  the  current  flowing  in  the  armature  depends, 

1  Swoope,  p.  362;  Rowland,  p.  230;  Franklin  and  Esty,  Dynamos  and  Motors,  p.  256. 


138  RADIO    COMMUNICATION. 

not  only  on  the  magnitude  of  the  current,  but  also  on  its  phase 
relation  to  the  emf.,  which  is  indicated  by  the  power  factor.  A 
lagging  current  causes  a  greater  reduction  in  terminal  voltage  than 
the  same  number  of  amperes  in  phase,  the  effect  increasing  with 
the  lag.  Thus  at  80  per  cent  power  factor  it  may  be  twice  as  great 
as  at  100  per  cent.  Conversely,  a  leading  current,  such  as  is  taken 
by  condensers,  improves  the  regulation,  so  that  the  terminal  voltage 
may  actually  be  higher  when  current  is  flowing  than  when  there  is 
none. 

84.  Effect  of  Speed  on  Regulation. — Since  the  emf.  is  proportional 
to  the  rate  of  cutting  of  flux,  it  follows  that  fluctuations  of  speed 
are  attended  with  proportional  fluctuations  of  voltage,  provided 
the  field  excitation  is  not  changed  at  the  same  time. 

85.  Voltage  Control. — The  simplest  way  to  control  the  voltage 
of  a  generator  is  by  adjusting  the  strength  of  the  magnetic  field 
by  means  of  the  field  current.     For  this  purpose  an  adjustable 
resistance  is  inserted  in  the  circuit  of  the  latter,   called  a  field 
rheostat. 

One  kind  consists  of  a  quantity  of  wire  of  an  alloy  having  a 
comparatively  high  resistance,  mounted  on  insulating  supports 
in  a  perforated  iron  box  with  a  slate  face,  or  embedded  in  an  insu- 
lating enamel.  A  handle  is  provided  for  making  contact  with  any 
one  of  a  number  of  brass  studs  attached  to  the  resistance  wire  at 
various  points,  so  that  more  or  less  of  it  can  be  in  circuit.  Ter- 
minals are  provided  for  connecting  the  rheostat  to  the  field  circuit. 
Fig.  109  shows  the  principle. 

The  place  of  the  field  rheostat  in  the  scheme  of  connections  is 
seen  in  Fig.  110,  which  represents  the  stationary  armature  and 
revolving  field  of  an  alternator,  with  arrangements  for  supplying 
current  to  the  alternator  field  from  the  exciter  E,  current  being 
controlled  by  the  field  rheostat  R. 

Small  alternators  for  field  use  in  radio  telegraphy  are  often  used 
without  a  field  rheostat.  The  voltage  is  kept  steady  enough  for 
practical  purposes  by  driving  the  machine  at  the  right  speed. 

C.  Direct  Current  Generators. 

86.  Commutation. — Fig.  102,   page  124,  illustrates  the  principle 
used  when  alternating  currents  are  generated  by  revolving  an  arma- 
ture in  a  stationary  magnetic  field.    But  if  each  end  of  the  loop  is 


RADIO   COMMUNICATION. 


139 


connected  to  a  half  cylinder  of  metal  (C,  Fig.  Ill),  on  which  rests  a 
stationary  brush  B+  or  B  — ,  than  as  the  loop  is  revolved  the  con- 
nection to  the  external  circuit  is  reversed  every  half  revolution,  and 
the  pulsations  of  current  are  always  in  the  same  direction.  The 
reversing  device  is  called  a  "commutator."  The  brushes  must  be 


Fiq.tos 


FieU 

Letters     correspond     in    the  "two    -fLkures 
PP-  Bind  ink    boats  A  -  ConT5ct  Arm 

5S-ContAeT  Studs  R  -  ResistAnce.  wi'r«s 


EL-  E-xc'iter  ArmoTu 
K  -Altern*tor  --ie 


Connection*    df    Alternator 


F-  Alternator    fieW  ooi  li 
A-  "  Armature 


so  set  that  the  reversal  of  connections  occurs  at  the  instant  when  the 
current  in  the  loop  is  zero  and  about  to  reverse. 

Thus  in  the  figure,  a  is  near  the  N  pole,  and  if  it  is  coming  toward 
the  reader  the  emf.  will  be  toward  the  right.  At  that  instant  the 
current  will  flow  out  through  the  segment  in  contact  with  the  upper 
brush  to  the  external  circuit;  that  is,  the  upper  brush  is  +.  After 
a  quarter  revolution  the  conductors  will  be  moving  along  the  flux: 


140 


RADIO    COMMUNICATION. 


and  not  cutting  across  it,  so  there  will  be  no  emf .  Each  brush  will 
be  just  in  the  act  of  passing  from  one  segment  to  the  other. 

After  a  half  revolution  from  the  position  shown,  b  will  have  ex- 
changed places  with  a.  Now  the  emf.  in  6  will  be  toward  the  right, 
and  current  will  flow  out  to  the  external  circuit  through  B+.  Thus 
the  same  brush  is  always  positive.  In  the  external  circuit  the  cur- 
rent always  flows  in  the  same  direction,  though  in  the  armature 
conductors  the  current  is  alternating. 

If  an  emf.  curve  similar  to  Fig.  95,  p.  116,  were  plotted  for  this  cir- 
cuit, with  time  measured  along  the  horizontal  axis,  and  volts  at  any 


pia.  ill 


'  -  Revolving  leof>  df  wire  &*.&-, 

X  -  External  circuit 


Production   oj  um-di'r«»c.t lonal  enrvf.   by  revolving  co'il   with 

NS  -   Ma£,n«t  C- Commute  tor,  Two 


j 
j,1 

^  ? 
I 


FIG   H'Z-      x-_. --' 

R'e.etificdtion  of  current. 

i   half-wave  Z    changed  To   t>eaitive   ri^lf -w^ve  3 


instant  along  the  vertical  axis,  the  result  would  be  somewhat  like 
Fig.  112.  Instead  of  a  positive  and  a  negative  half  wave,  there 
would  be  two  positive  halves,  the  negative  being  rectified  by  means 
of  the  commutator. 

Again,  as  with  alternators,  the  need  of  higher  emfs.  than  can  be 
developed  by  a  single  loop,  and  of  more  effective  utilization  of  the 
material,  make  necessary  the  use  of  coil- wound  armatures  and  multi- 
polar  field  magnets.  With  a  commutator  consisting  of  only  a  few 


RADIO   COMMUNICATION. 


141 


segments,  say  as  many  segments  as  there  are  magnet  poles,  the  cur- 
rent would  still  be  pulsating. 

To  get  a  steady,  practically  constant  emf.,  commutators  are  used 
having  many  segments — several  hundred  in  the  case  of  large  gen- 
erators and  motors,  and  usually  not  fewer  than  20  or  30  even  on  very 
small  machines  for  110-volt  circuits.  Such  a  commutator  consists 
of  bars  of  copper,  slightly  wedge-shaped,  separated  by  thin  insu- 
lating sheets  of  mica,  the  whole  assembled  in  the  form  of  a  cylinder 
held  together  by  strong  end  clamps.  The  segments  are  insulated 
from  the  clamps  by  suitably  shaped  rings,  usually  of  molded  mica 
insulation.  Connections  leading  to  the  armature  conductors  are 


:    of   A  -\po\a.    Drum   Wl.nehn^ 
1, 1, 3. etc.    CornmotAtor  -.e^rn-nta  r  -  -h  -   Location*   of  brushes 


soldered  into  slots  in  the  segments,  which  commonly  have  lugs  or 
"risers"  for  the  purpose,  extending  upward  at  the  end  toward  the 
armature. 

87.  King  and  Drum  Windings. — Armature  windings  fall  into  two 
broad  classes,  called  "ring"  and  "drum"  windings,  according  to 
the  way  the  conductors  are  mounted  on  the  core.  In  the  first  of 
these  the  wire  is  laid  on  the  outside  and  passed  through  the  hollow 
space  inside  of  the  core,  being  threaded  through  and  through  much 
as  a  napkin  ring  or  a  bridle  ring  might  be  covered  with  string. 

Ring  windings  are  scarcely  ever  used  nowadays.  Modern  ma- 
chines have  windings  of  the  type  shown  in  Fig.  113,  called  "drum" 


142  RADIO    COMMUNICATION. 

windings.  The  conductors  are  all  on  the  outer  face  of  the  core, 
and  the  two  branches  of  a  turn  lie  under  adjacent  poles,  of  oppo- 
site polarity.  These  two  features  are  characteristic  of  all  kinds  of 
drum  winding.  In  the  kind  illustrated  in  the  diagram,  starting 
with  commutator  segment  1,  we  pass  up  to  conductor  b,  which  at 
the  instant  shown  is  under  a  S  pole.  It  is  connected  at  the  back 
of  the  armature  to  i,  which  lies  under  a  N  pole  and  is  soldered  into 
segment  2.  Starting  at  2,  we  have  d  under  the  edge  of  the  S  pole 
back-connected  to  k  under  the  edge  of  the  N  pole;  k  is  attached  to 
segment  3.  Continuing  in  the  same  way  all  around  the  armature 
we  finally  have  16  loops  connected  to  the  16  commutator  segments. 
It  will  be  understood  that  an  actual  machine  has  a  great  many  more 
turns  in  the  armature  winding  and  a  larger  number  of  commutator 
segments. 

At  the  four  segments  marked  +  or  — ,  contact  is  made  with  brushes 
leading  to  the  external  circuit.  By  the  '  'right-hand  rule  "  the  emf . 
in  conductors  under  the  N  pole  is  toward  the  back  end,  so  current 
flows  into  the  armature  at  segment  3.  The  brush  on  that  segment 
is  therefore  negative.  The  brush  at  segment  7  is  positive,  because 
there  the  current  flows  out  of  the  armature.  Similar  reasoning 
applied  to  the  conductors  under  the  S  poles  leads  to  the  same  result 
as  to  polarity  of  the  brushes,  which  are  thus  seen  to  be  alternately, 
one  positive  and  the  next  negative,  as  we  go  around  the  commutator. 
If  a  machine  having  more  than  two  sets  of  brushes  is  examined  it 
will  be  found  that  all  the  positive  brushes  are  joined  by  a  heavy 
conductor  and  all  the  negative  brushes  by  another.  Then  one  con- 
nection is  made  from  the  group  of  positive  brushes  to  the  external 
circuit,  and  one  from  all  the  negative  brushes. 

In  speaking  of  alternators,  the  actual  construction  of  armatures 
was  described;  that  is,  the  use  of  machine-wound  coils  in  slots  in  the 
face  of  a  laminated  core.  D.c.  armatures  are  made  the  same  way 
except  that  the  ends  of  the  coils  are  soldered  to  the  commutator 
segments.1 

The  main  steps  are  shown  in  Figs.  114,  115,  and  116.  The  first 
shows  the  copper  segments,  with  their  sheets  of  mica  between  them, 
assembled  in  the  form  of  a  ring  and  held  together  by  a  firm  tem- 
porary clamp.  The  next  picture  shows  the  commutator  fastened  on 
the  front  end  of  the  armature  core.  The  "risers"  are  to  be  seen 

1  Brief  information  on  the  care  of  commutators  and  proper  position  of  brushes  is 
given  at  the  end  of  this  chapter  in  Sec.  106  on  "Common  troubles." 


FIG.  114.— (Upper)  Method  of  assembling  commutator  segments.  Fig.  115.- 
(Middle)  Commutator  and  armature  core  assembled  showing  risers.  Fig.  llft.- 
(Lower)  Armature  complete  with  windings  connected  to  risers. 

143 


144 


RADIO    COMMUNICATION. 


coming  up  from  the  ends  of  the  segments  for  connection  to  the  arma- 
ture coils.  On  the  core,  built  up  of  thin  laminations,  note  the  teeth, 
slots,  and  three  rows  of  air  ducts  for  ventilation.  The  last  picture 
shows  the  coils  in  the  slots  of  the  core.  Their  ends  have  been  sol- 
dered to  the  commutator. 

88.  Excitation:  Separate,  Series,  Shunt,  Compound. — While  alter- 
nators require  d.c.  from  a  separate  source  for  their  field  excitation, 
direct  current  dynamos  excite  their  own  fields.  Depending  on  the 
scheme  of  connections  between  the  armature  and  the  field  coils,  this 


to 


FlO.    117 

Various    modes    of 
CxcitYn,*,  d.  C.^enewTor.5 

A  -  .armature. 

F-  Fine,  wire  orshont- 
f.eld    wmd.n^ 


.Shunt 


Compound 


gives  rise  to  several  arrangements,  all  of  which  are  of  practical  im- 
portance. In  this  discussion  we  leave  out  of  consideration  the 
"magneto",  which  depends  for  its  magnetic  field  on  a  group  of 
permanent  magnets. 

Fig.  117  shows  the  several  ways  of  exciting  the  field  magnets, 
and  incidentally  illustrates  the  conventional  symbols  generally  used 
for  an  armature  and  for  field  windings.  In  this  sort  of  diagram  no 
attempt  is  made  to  draw  a  picture  of  the  machine.  A  whole  set  of 


RADIO  COMMUNICATION.  145 

field  coils,  for  example,  is  represented  by  a  single  coil,  the  armature 
and  brushes  by  a  single  circle1  and  two  strokes. 

Separate. — The  first  sketch  indicates  that  current  for  the  field  coils 
comes  from  a  source,  like  a  battery,  entirely  independent  of  the 
armature.  Such  a  machine  is  said  to  be  "separately  excited." 

Shunt. — The  next  indicates  that  the  current  from  the  armature 
divides;  some  goes  to  the  load  circuit,  some  to  the  field  coils;  the  two 
unite  again  and  flow  back  into  the  armature  at  the  brush  of  opposite 
polarity.  When  the  current  from  the  armature  divides,  a  portion 
flowing  through  the  field  winding,  the  machine  is  spoken  of  as  a 
'  'shunt  generator.  "  Only  a  small  fraction  of  the  total  current  which 
a  machine  is  able  to  generate  continuously  is  required  for  shunt  field 
excitation;  it  may  be  5  or  6  per  cent  for  a  1-kw.  generator,  and  as 
little  as  perhaps  2  per  cent  for  a  100-kw.  generator. 

Shunt  field  windings  consist  of  many  turns  of  fine  wire  (insulated, 
of  course).  There  may  readily  be  2000  or  3000  turns.  For  in- 
stance, the  little  exciter  for  the  500-cycle  audio  frequency  generator 
described  on  p.  152,  is  a  direct  current  shunt  generator.  Each  of  its 
two  field  coils  has  2800  turns  of  wire  about  0.25  mm.  (0.01  in.)  in 
diameter.  Using  this  great  quantity  of  fine  wire  has  two  conse- 
quences; because  of  its  high  resistance  it  lets  only  a  small  current 
flow;  because  of  the  large  number  of  turns  this  small  current  suffices 
to  produce  the  desired  magnetomotive  force  (which  depends  on  the 
''ampere  turns"). 

Series.-  -When  the  whole  current  from  the  armature  flows  through 
the  field  coils,  the  generator  is  "series  excited."  Two  ways  of  repre- 
senting a  series  generator  are  shown  in  Fig.  117.  Heavy  wire  is 
used  for  series  coils.  They  have  to  carry  the  full  current  output  of 
the  machine;  fine  wires  would  overheat  and  destroy  the  insulation. 
The  necessary  ampere  turns  are  secured  by  virtue  of  having  a  large 
number  of  amperes  and  comparatively  few  turns  of  wire. 

Compound. — When  a  generator  is  provided  with  two  sets  of  field 
coils,  one  of  fine  wire  connected  in  shunt  and  the  other  of  a  few  turns 
of  heavy  conductor  connected  in  series  with  the  armature,  it  is  called 
a  "compound  wound"  generator,  or  more  commonly  just  a  "com- 
pound" generator.  Two  ways  of  representing  it  are  shown  in 
Fig.  117. 

i  Note  difference  from  alternator,  which  has  two  circles,  representing  slip  rings. 
97340°— 19 10 


146  RADIO    COMMUNICATION. 

89.  Characteristics  of  Terminal  Voltage. — Why  are  so  many 
different  kinds  of  connection  used  for  field  excitation?  Ordinarily 
the  load  on  a  generator  will  vary.  By  this  we  mean  that  there  are 
changes  in  the  number  of  devices  switched  on;  lamps  may  be 
turned  on  or  off,  or  motors  started  and  stopped.  Such  changes  of 
load  automatically  affect  the  terminal  voltage  of  the  generator,  but 
they  affect  it  differently,  according  to  the  kind  of  field  excitation 
used. 

To  see  why  the  effects  differ,  in  each  case  consider  the  dynamo 
driven  at  a  steady  speed  without  load.  Then  imagine  the  load  (cur- 
rent through  the  armature)  to  be  successively  increased.  If  sepa- 
rate excitation  is  used,  a  certain  emf .  is  generated  at  no  load.  When 
current  flows  in  the  armature,  some  of  this  emf.  is  used  up  in  sending 
the  current  through  the  resistance  of  the  armature  itself.  There  is 
also  another  effect,  due  to  "armature  reaction,"  l  which  weakens  the 
magnetic  field.  Both  increase  as  the  armature  current  increases. 
Hence  the  terminal  volts  are  less  when  the  armature  current  is  large, 
than  when  it  is  small.  Curve  a,  Fig.  118,  shows  this  graphically. 
The  load  current  in  amperes  is  plotted  along  the  horizontal  axis, 
the  terminal  volts  along  the  vertical  axis.  The  greater  the  current, 
the  lower  the  voltage.  The  difference  between  no  load  and  full 
voltage  shown  in  the  diagram  corresponds  to  a  regulation  2  of  some 
8  per  cent,  and  applies  to  rather  large  machines,  say  of  100  kw.  or 
more.  For  a  smaller  one,  the  difference  would  be  greater. 

When  shunt  excitation  is  used  the  reduced  terminal  voltage  sends 
a  reduced  current  through  the  field  coils,  so  the  magnetic  flux  is 
weaker,  the  greater  the  armature  current.  Hence  the  terminal 
voltage  falls  off  more  than  it  does  with  separate  excitation.  Thus 
curve  6,  Fig.  118,  droops  more  than  curve  a.  The  dashed  part 
shows  how  the  voltage  falls  off  when  the  machine  is  greatly  over- 
loaded. 

With  series  excitation,  the  condition  is  very  different.  When  no 
current  flows,  only  the  weak  residual  magnetism  of  the  iron  is  avail- 
able, and  the  emf.  generated  is  consequently  very  small.  Curve  c 
shows  it  by  starting  only  a  very  little  above  the  zero  value.  If 
current  is  taken  from  the  machine,  this  current,  flowing  in  the  field 

1  Armature  reaction  is  explained  in  Section  82  and  also  in  Franklin  and  Esty's 
Elem.  of  E.  E.,  vol.  l,p.  151;  Franklin  and  Esty,  Dynamos  and  Motors,  p.  176;  Timbie 
and  Higbie,  Direct  and  Alternating  Currents. 

2  Denned  in  Section  81. 


RADIO   COMMUNICATION. 


147 


coils,  strengthens  the  magnetic  field  and  so  causes  a  greater  emf.  to 
be  generated.  The  greater  the  current  taken  by  the  external  cir- 
cuit, the  greater  will  be  the  voltage.  Hence  curve  c  rises. 

In  the  compound  generator  the  two  effects  are  combined.  De- 
pending on  the  relative  proportions  of  the  two  windings,  the  voltage 
at  full  load  may  be  made  equal  to  that  at  no  load,  or  greater,  or  less; 
the  latter  is  rare.  Curve  d.  Fig.  118,  is  for  a  generator  somewhat 


LoAd,    Percent  of  rated     Am^res 

Fiq.  lift 

Delation   between  Current  Output  and"  Termi'nal    Volts 
A  -  For  Ae(3Ar<ately    excited   generator 
b-    For  ihunT  £pncrA\or 
C-   For  Series  £5enera"tbr 
d-   For   Corr,|3oi>nd    £ener«»1br 


"over-compounded."     If  the  full  load  voltage  were  the  same  as  the 
no  load  voltage,  the  generator  would  be  "flat-compounded." 

In  examining  a  generator,  it  is  usually  impossible  to  determine 
whether  the  field  coils  are  of  fine  or  thick  wire  without  tearing  them 
open,  because  they  are  protected  with  wrappings  of  tape,  hard  cord, 
or  other  covering.  To  distinguish  between  shunt  and  series  coils  is, 
however,  quite  easy  by  looking  at  the  connections.  Those  between 
the  shunt  field  coils  on  the  different  poles  are  small  because  they 
have  to  carry  only  a  small  current,  those  between  the  series  coils  are 


148  RADIO    COMMUNICATION. 

heavy,  consisting  of  thick,  wide  straps  of  copper  on  the  larger  gener- 
ators. 

90.  Emf.  Equation.  —  It  has  been  stated  that  the  emf.  developed 
in  a  conductor  depends  on  the  rate  of  cutting  the  magnetic  flux  ' 
and  is  equal  in  volts  to  the  number  of  magnetic  lines  of  force  cut  per 
second,  divided  by  108.  On  an  armature  a  number  of  such  con- 
ductors are  connected  in  series  and  their  emfs.  are  therefore  added. 
Thus  in  Fig.  113,  the  conductors  which  would  have  to  be  traversed 
in  going  from  one  brush  on  the  commutator  to  the  next  through  the 
armature  constitute  one  such  group.  There  are  three  other  similar 
paths,  and  these  four  paths  are  all  in  parallel,  so  the  resulting  emf. 
is  the  same  as  that  of  one  path  alone,  but  the  current  that  goes  to  the 
external  circuit  is  the  sum  of  the  currents  in  the  four  paths. 
Let  JV=the  number  of  conductors  in  series. 

n=mimber  of  revolutions  per  second  (not  per  minute)  of  the 
armature. 

2>=number  of  magnetic  poles. 

</>=magnetic  flux  per  pole. 

Then  the  flux  cut  per  second  by  any  conductor  is  nXpX<i>  lines. 
Dividing  by  108  gives  the  average  volts.  If  there  are  N  conductors 
in  series,  the  total  emf.  is 

(6S) 


This  formula  shows  that  the  voltage  of  a  generator  can  be  changed 
by  changing  the  speed  n,  the  flux  </>,  the  number  of  poles  p,  or  the 
number  of  conductors  N.  The  last  two,  of  course,  are  fixed  once  for 
all  when  the  machine  is  built;  the  first  two  can  be  changed  quickly 
by  the  operator,  and  afford  practical  means  of  controlling  the  voltage. 

This  formula  means  exactly  the  same  thing  as  the  one  given  for 

induced  emf.  in  Chapter  1,  namely  that  E=—^-     It  is  merely  nec- 

t 

essary  to  note  that  if  nXp  poles  are  passed  per  second,  then  the  time 
required  to  cut  the  flux  <f>  is  only  —  -7—  th  of  a  second;  this  takes  the 

71  X  P 

place  of  t  in  the  denominator;  or  what  amounts  to  the  same  thing  as 
dividing  by  ———,  we  multiply  by  nXp.     The  reason  for  the  factor 
108  in  the  denominator  has  been  explained. 
i  Chapter  1,  Section  45. 


RADIO   COMMUNICATION.  149 

91.  Voltage  Control. — The  practical  way  of  controlling  the  voltage 
of  separately  excited,  shunt  and  compound  generators  is  by  having 
an  adjustable  resistance,  called  a  "field  rheostat"  (Fig.  109),  in  cir- 
cuit with  the  fine  wire  (shunt  field)  coils.     The  points  R  in  Fig. 
117,  show  where  such  a  rheostat  might  be  put  in  the  circuit  of  each 
machine. 

92.  Effect  of  Varying  Speed. — A  rise  or  fall  of  speed  causes  the 
emf .  of  a  separately  excited  generator  to  rise  or  fall  in  about  the  same 
proportion.     In  shunt  and  compound  generators  the  effect  is  greater. 
That  is  why  engines  for  driving  such  generators  have  to  have  good 
governors,  if  a  steady  voltage  is  wanted. 

Because  of  these  characteristics,  each  type  of  generator  has  its 
special  uses.  For  instance,  the  exciter  for  the  a.c.  generator  of  a 
radio  field  set  is  a  simple  shunt  generator,  because  the  load  does  not 
change  much.  The  shunt  generator  is  good  also  for  charging  storage 
batteries.  Incandescent  lamps  need  a  very  steady  voltage  that  is 
not  changed  when  some  of  them  are  turned  on  or  off.  A  compound 
generator  meets  this  requirement. 

D.  Special  Alternators  for  Radio  Use. 

93.  Audio   Frequency  and  Radio  Frequency. — Alternating   cur- 
rents are  generated  at  various  frequencies,  covering  a  remarkably 
wide  range.     Depending  on  their  application,  the  frequencies  in 
practical  use  fall  into  three  well  defined  classes: 

(a)  Commercial  frequencies,  which  nowadays  generally  mean  25 
or  60  cycles  per  second. 

(b)  Audio  frequencies,  around  500  to  1000  cycles  per  second. 

(c)  Radio  frequencies,   usually  between  100,000  and  1,000,000, 
but  extending  in  extreme  cases  down  to  perhaps  10,000  and  up  to 
several  million  cycles  per  second. 

Commercial  frequencies  are  used  for  lighting  and  power.  The 
great  machines  in  the  central  stations  which  supply  our  cities  with 
current  operate  at  these  frequencies. 

Audio  frequencies  are  those  conveniently  heard  in  the  telephone. 
When  alternating  currents  are  sent  through  a  telephone,  the  dia- 
phragm of  the  latter  vibrates.  The  vibrations  are  heard  as  sound. 
The  more  rapid  the  vibrations,  the  shriller  the  tone.  Vibrations  at 
the  rate  of  4000  or  5000  per  second  give  a  shrill  whistle,  while  the 
lowest  notes  of  a  bass  voice  have  somewhat  under  100.  If  a  500- 
cycle  generator  supplies  current  to  a  spark  gap  and  the  spark  jumps 


150  RADIO    COMMUNICATION. 

once  on  the  positive  and  once  on  the  negative  half-wave,  then  at 
the  receiving  station,  the  signal  is  heard  in  the  telephone  as  a 
musical  tone  of  1000  vibrations  per  second. 

Radio  frequencies  occur  in  the  circuits  of  radio  apparatus,  for 
instance  in  an  antenna.  They  are  too  rapid  to  cause  a  sound,  in  a 
telephone,  which  can  be  heard  by  the  human  ear.  They  may  be 
generated  by  dynamo-electric  machines  of  highly  specialized  con- 
struction, but  are  usually  produced  by  other  means. 

94.  Audio  Frequency  Generators. — To  show  how  the  methods 
described  in  the  preceding  sections  are  applied  in  actual  generators, 
a  few  typical  machines,  used  in  radio  sets,  will  be  briefly  descibed. 
Whether  or  not  these  are  of  the  latest  design  is  not  important. 
Changes  of  detail  are  constantly  being  made,  but  they  do  not  affect 
the  principles  used  and  can  be  readily  understood  after  the  workings 
of  similar  machines  have  been  grasped.  The  examples  of  machines 
here  given  will  also  illustrate  how  the  form  of  generator  and  the 
auxiliaries  used  with  it  are  influenced  by  the  source  of  power  avail- 
able for  driving  it. 

The  generator  is  only  one  part  of  a  unit  for  converting  energy  into 
the  electrical  form.  The  other  part  depends  on  the  source  of  energy 
available;  it  may  be  heat  derived  from  coal  or  gasoline;  it  may  be 
falling  water,  moving  air,  human  muscles,  or  a  charged  storage  bat- 
tery. 

Crank  Driven. — The  field  radio  pack  set  furnishes  an  example  of 
a  self-contained  generating  unit  driven  by  hand.  These  sets  have 
been  changed  somewhat  from  time  to  time  and  can  therefore  be 
described  only  in  a  general  way.  The  generator  is  cylindrical  in 
shape  and  is  entirely  incased,  including  the  ends,  in  a  metal  shell. 
At  one  end  of  it  is  a  flywheel  for  equalizing  the  speed.  At  the  other 
is  the  train  of  gears,  running  in  oil  and  inclosed  in  a  housing, 
through  which  power  is  transmitted  from  the  crank  shaft  to  the 
generator  shaft.  The  crank  shaft  is  turned  by  means  of  a  pair  of 
cranks. 

The  alternator  is  a  250-watt,  500-cycle  machine  of  the  revolving 
armature  type.  The  exciter l  is  built  in  with  the  alternator,  so  that 
the  two  have  but  one  frame  and  one  set  of  bearings,  and  the  same 
shaft  carries  both  armatures.  Near  one  end,  on  opposite  sides  of 
the  shell,  is  a  pair  of  holes  giving  access  to  the  d.c.  brushes  which 
bear  on  the  commutator  of  the  exciter  2  and  near  the  other  end  are 

1  A  little  generator  of  d.  c.  for  the  fixed  coils  of  the  alternator.    See  Sec.  71. 

2  The  commutator  is  described  in  Sec.  86. 


RADIO  COMMUNICATION. 


151 


similar  holes  for  the  a.c.  brushes  that  bear  on  the  collector  rings. 
The  crank  is  turned  at  the  rate  of  33  to  50  r.p.m.,  depending  on  the 
machine  (that  is,  the  date  of  the  model),  and  the  generators  make 
3300  to  5000  r.p.m.,  the  cranks  being  geared  to  them  at  a  ratio  of  1 
to  100. 

The  diagram  and  data  of  Fig.  103  apply  to  the  alternator  of  such 
a  set,  the  armature  having  18  teeth,  the  same  as  the  number  of  field 


FlQ.119 

Connections  of 


D  -  exciter  ArrrvsTure 
C5"  A-C  £jeneraTor    " 
E.F-  Exciter  field 
A  F-  Alternator  -field 
Pi  Pz"^0^  connections 
K  -  "Sendm^    Key 
T  -  Coil  of  Transformer 


Ex.f leld  rheo.  Qen. field  rheo 


e  A.C 


Sch 


j  c 


nection    o}  a  Tractor  .Set 
And     exciter 


poles.     To  get  500  cycles  it  must  make  3333  r.p.m.,  which  corre- 
sponds to  a  crank  speed  of  about  33  r.p.m. 

The  connections  are  shown  in  Fig.  119.  The  field  coils  of  the 
exciter  are  connected  directly  to  the  brushes.  The  circuit  to  the 
alternator  field  coils  passes  through  a  receptacle  Pt  on  the  side  of  the 
machine.  A  two-wire  cable  can  be  plugged  in  at  this  point,  for  the 
sending  key.  While  the  key  is  closed,  field  current  flows  and  a.c.  is 


152  RADIO    COMMUNICATION. 

generated  in  the  armature.  Another  receptacle  P2  provides  for 
connecting  the  alternator  armature  to  the  transformer  from  which 
current  is  supplied  for  the  spark. 

In  view  of  the  high  speed  at  which  these  generators  run  (some 
make  5000  r.p.m.)  the  brushes  have  to  fit  very  smoothly  and  the 
bearing  surfaces,  particularly  the  d.c.  commutator,  have  to  be  in 
good  condition.  For  ease  of  turning,  they  should  not  be  pressed  in 
harder  than  necessary;  on  the  other  hand,  unless  the  contact  is  good, 
the  set  fails  to  operate  satisfactorily.  The  most  common  troubles, 
•electrically,  are  due  to  a  dirty  commutator,  poor  brush  contacts,  or 
to  turning  the  brushes  in  replacing  them,  so  that  the  curve  of  the 
brush  does  not  match  the  curve  of  the  commutator. 

Gasoline  Engine  Driven. — Hand  power  is  not  practical,  except 
for  very  small  generators,  since  a  man  can  develop  only  about  one- 
tenth  of  a  horsepower  if  he  has  to  keep  it  up  for  more  than  a  short 
time.  One  of  the  most  convenient  sources  of  larger  power  is  the 
gasoline  engine.  It  is  particularly  suitable  for  isolated  stations,  or 
for  the  more  powerful  portable  sets,  like  the  field  radio  tractor  sets. 
Detailed  information  about  any  particular  set  is  supposed  to  be 
furnished  with  the  set,  but  certain  features  are  likely  to  be  common 
to  all. 

The  speed  of  rotation  of  the  alternator  is  almost  always  much 
higher  than  that  of  an  engine;  it  is  therefore  stepped  up  by  pulleys 
and  belts,  or  sprockets  and  chain,  or  gears,  the  smaller  pulley  or 
sprocket  or  gear  being  on  the  generator  shaft. 

The  generator  may  be  of  any  of  the  three  possible  types  previously 
described;  for  example,  one  of  the  permanent  Signal  Corps  stations 
uses  an  inductor  alternator  (Sec.  74);  one  kind  of  tractor  set  also 
has  the  inductor  type;  another  has  the  revolving  armature.  If  it 
becomes  necessary  to  open  the  machine,  it  is  easy  to  discover  which 
type  it  is.  If  the  rotor,  or  revolving  part,  has  no  windings  at  all. 
then  we  are  dealing  with  an  inductor  alternator;  if  the  circuit  lead- 
ing to  the  transmitting  apparatus  (not  necessarily  the  key,  be- 
cause that  may  be  in  the  field  circuit)  comes  from  the  slip  rings, 
then  the  revolving  part  must  be  the  armature. 

In  one  of  the  sets  of  this  latter  type  the  alternator  and  its  exciter 
are  two  separate  machines,  connected  by  a  coupling  so  that  both 
revolve  together.  A  frequency  indicator  in  front  of  the  chauffeur 
guides  him  in  controlling  the  speed  of  the  engine  so  as  to  maintain 
the  right  frequency — 500  cycles  per  second.  The  combination  is 
chain  driven  from  the  main  transmission.  The  same  engine  that 


RADIO  COMMUNICATION.  153 

drives  the  truck  is  used  to  furnish  power  for  the  generator,  the  one 
or  the  other  being  thrown  in  as  desired. 

The  following  name  plate  data  of  this  particular  set  will  illustrate 
some  of  the  statements  made  in  earlier  sections: 

Generator  frequency,  500  cycles;  poles,  30;  kva.,  2.5;  open  cir- 
cuit volts,  245 ;  loaded  key  volts,  110;  2kw.  atO.SOp.f.;  2000  r.p.m. 

Exciter,  shunt  type:  poles,  2;  load  volts,  110;  load  amperes,  2.7; 
0.3  kw. 

From  the  speed,  2,000  r.p.m.,  and  the  stated  number  of  poles, 
30,  each  revolution  gives  15  cycles  and  the  cycles  per  second  will  be 
15X2,000/60=500,  which  checks  with  the  figure  given. 

From  the  loaded  key  volts,  110,  and  the  rating,  2.5  kilovolt-am- 
peres  or  2500  volt-amperes,  the  full  load  current  is  2500/110  or  22.7  am- 
peres. The  product  of  volts,  amperes,  and  power  factor  gives  power 
in  watts;  thus  110X22.7X0.80=2000  watts,  or  2  kw.  The  great 
difference  between  the  volts  on  open  circuit,  245,  and  volts  when 
loaded,  110,  shows  that  the  armature  has  a  high  impedance.  It 
must  not  be  assumed  that  this  loss  of  voltage  is  all  due  to  resistance, 
and  so  represents  a  waste  of  power.  Much  of  it  is  due  rather  to  the 
demagnetizing  action  mentioned  in  Section  82,  which  causes  a  reduc- 
tion in  the  effective  magnetism  and  therefore  in  the  emf .  generated. 

The  scheme  of  connections  in  Fig.  120  shows  that  the  exciter 
voltage  can  be  controlled  by  means  of  the  exciter  field  rheostat.  This, 
in  itself,  would  govern  the  500-cycle  voltage  fairly  well,  but  a 
second  control  is  provided  in  the  generator  field  rheostat.  High- 
resistance  connections  between  each  machine  and  the  ground  pro- 
vide a  leakage  path  for  high  voltage  charges  and  prevent  their 
accumulation. 

Fan  Driven. — Audio  frequency  generators  have  an  important 
application  in  furnishing  current  for  communicating  from  airplanes. 
Fan  motors  have  been  used  as  a  source  of  power,  though  it  has  been 
objected  that  they  increase  the  head  resistance  of  the  plane.  There 
is  no  theoretical  reason  why  any  type  of  self-contained  generator 
might  not  be  used,  but  because  of  the  high  rotative  speeds  obtainable 
with  fans  and  the  need  of  lightness,  special  machines  have  been 
developed  with  the  fan  mounted  directly  on  an  extension  of  the 
shaft.  One  very  recent  form  is  described  on  page  159. 

Motor  Driven,  by  A.C.  Motor. — When  electric  current  is  to  be 
had,  but  not  at  the  desired  frequency,  use  may  be  made  of  a  com- 
bination of  a  motor,  adapted  to  the  circuit  that  is  available,  and  a 
500-cycle  generator.  Such  a  combintion  is  called  a  "motor-generator 


154 


RADIO    COMMUNICATION. 


set."  For  use  with  110- volt,  60-cycle  alternating  current,  sets  are 
built  using  the  same  sort  of  generator  (with  built-in  exciter)  described 
in  connection  with  hand  driven  apparatus.  Mounted  on  a  common 


FIG.  121.— Small  500-cycle  motor-generator  set  (2500  r.p.m.;  24  poles  oa  stator; 
24  teeth  on  rotor;  110  volts;  3.2  amp.;  0.35  kva.) 


1.  Field  terminals. 

2.  Collector  rings. 


3.  Armature  terminals. 

4.  Shaft  of  both  units. 


bedplate  with  it  is  an  a.c.  motor.     The  shafts  are  connected  by  a 
flexible  coupling. 

Except  for  the  mechanical  connection  between  the  shafts,  the  two 
machines  are  entirely  independent.  Electrically  there  is  no  connec- 
tion. The  motor  is  designed  to  run  automatically,  at  the  proper 
speed  for  the  generator,  or  perhaps  it  would  be  better  to  say  that  there 
are  certain  definite  speeds  at  which  60-cycle  a.c.  motors  have  to 


Fio.  122. — Motor-generator  set  of  Fig.  121  partly  dismantled. 


Motor  brushes. 

Motor  field  windings. 

Motor  field  poles. 

Motor  field  yoke. 

Terminals  of  motor  field  windings. 

Motor  armature  core. 

Commutator. 

Generator  armature  windings. 


9.  Generator  armature  core. 

10.  Collector  rings. 

11.  Motor  armature  windings. 

12.  Generator  brushes. 

13.  Generator  field  windings. 

14.  Generator  field  yoke. 

15.  Terminals  of  generator  field  windii 


156 


RADIO    COM  MUN  1C ATIOX . 


run,  and  the  generator  has  such  a  number  of  poles  that  it  gives  the 
desired  frequency  when  driven  by  a  motor  operating  at  one  of  these 
speeds.  Voltage  control  of  the  generator  is  secured  by  means  similar 
to  those  shown  in  Fig.  120. 

Motor  Driven  by  D.  C.  Motor. — When  direct  current  at  110  volts  is 
available,  the  arrangement  is  somewhat  different.  The  exciter  is 
unnecessary,  because  current  for  the  field  coil  of  the  alternator  may 
be  taken  directly  from  the  line.  It  is  then  possible  to  combine  the 
generator  and  a  110-volt,  direct  current,  shunt  motor  (see  Sec.  97) 


Connection*     of  motor -generator  for  conversion   'from    D.  C.   To 
M~  Motor  Armature  E.,  -  Motor  -field   rheo 

Q  —  Generator  armature.  £•£  -  Generator  field 

5.E*  -  Motor  start.ni,  box 
OF-  Operator  field  winding 


into  a  very  compact  unit.  The  two  armatures  are  on  the  same  shaft 
and  the  two  frames  are  joined  in  one  structure. 

Fig.  121  represents  such  a  unit,  which  is  shown  partly  disas- 
sembled in  Fig.  122.  The  generator  happens  to  be  of  the  same 
design  as  that  shown  in  diagram  in  Fig.  103,  but  being  built  for 
nearly  50  per  cent  more  power,  it  is  spmewhat  larger,  has  more  poles, 
and  runs  at  a  correspondingly  lower  speed  to  give  the  same  fre- 
quency. The  two  armatures  are  seen  on  their  common  shaft;  the 
collector  rings  are  near  one  end  and  the  commutator  near  the  other. 

One  scheme  of  connections  for  such  a  unit  is  seen  in  Fig.  123, 
which  shows  the  d.c.  motor  connected  to  its  line  by  way  of  a  switch 


RADIO   COMMUNICATION. 


157 


and  starting  box.1  The  rheostat  shown  in  circuit  with  the  motor 
field  may  be  omitted.  Its  purpose  is  to  give  control  of  the  motor 
speed,2  if  such  control  is  desired,  in  order  to  get  some  definite  fre- 
quency quite  accurately  in  the  a.c.  circuit.  From  the  d.c.  line, 
connection  is  made  also  to  the  generator  field  winding,  the  flow  of 
current  being  controlled  by  another  rheostat  which  determines  the 
magnetization  and  therefore  the  generator  voltage.  Thus  the  gen- 
erator frequency  may  be  governed  by  means  of  the  motor  field 
rheostat  and  the  voltage  by  the  generator  field  rheostat. 

Motor  Driven  Inductor  Alternators. — Thus  far  in  this  part  of  the 
chapter,  attention  has  been  centered  on  revolving  armature  gener- 
ators. It  is  equally  feasible  to  generate  500-cycle  current  by  means 
of  inductor  alternators.  Fig.  124  represents  a  motor-driven  in- 
ductor alternator  for  conversion  from  direct  to  alternating  current 
at  500  cycles.  The  table  following  gives  the  data  as  taken  from 
the  name  plate. 

Name  plate  data  for  motor-generator  shown  in  Fig.  124 . 


D.C.  motor. 

A.C.  gener- 
ator. 

Volts  

120 

125 

Amperes        ... 

7.3 

5 

Revolutions  per  minute  

2500 

2500 

Rating  

1  h.p 

0.  625  kva. 

Shunt  field  amperes 

0.4 

Cycles  per  seconi  

500 

Here  again  the  two  distinct  machines,  motor  and  generator,  are 
combined  in  a  single  compact  unit.  The  armatures  are  on  one  shaft 
and  the  two  frames  are  made  into  one  structure,  though  openings 
are  left  for  ventilation.  These,  as  well  as  other  openings  at  the 
ends  of  the  machine,  are  screened  to  keep  out  foreign  material, 
while  permitting  a  free  flow  of  air  for  cooling.  The  generator  frame 
is  cast  in  the  form  of  a  cylindrical  shell.  At  each  end  is  inserted 
a  laminated  armature  core,  with  teeth  projecting  radially  inward, 
on  which  the  armature  winding  is  placed.  Between  the  two  arma- 


i  Described  in  Sec.  97. 


2  How  this  is  done  is  explained  in  Sec.  97. 


FIG.  124.— Inductor  alternator  type  motor-generator  set. 


1.  Generator  armature  coils,  first  row. 

2.  Generator  armature  coils,  second 

row. 

3.  Generator  field  coU. 

158 


4.  Terminal  box. 

5.  Inductor  teeth. 

6.  Brass  disks. 

7.  D.  c.  motor  armature. 


RADIO   COMMUNICATION.  159 

ture  cores  is  the  field  winding,  a  single  large  coil  which  fits  inside 
the  cylindrical  shell  where  it  is  rigidly  held  in  place.  This  coil 
produces  a  magnetic  flux  parallel  with  the  shaft.  The  armature 
winding  is  in  two  groups,  one  on  each  core.  Each  group  consists 
of  12  coils,  and  the  coils  are  all  connected  in  series. 

The  portion  of  the  set  so  far  described  is  stationary.  The  rotor 
is  a  solid  cylindrical  core,  at  each  end  of  which  is  a  ring  of  12  teeth 
projecting  radially  outward.  The  core  is  magnetized  by  the  sta- 
tionary field  winding  previously  mentioned.  To  trace  the  mag- 
netic circuit,  begin  at  the  core.  One  end  of  it  is  N.  the  other  S. 
The  flux  passes  out  through  all  the  rotor  teeth  at  the  N  end,  across 
the  air  gaps,  into  the  adjacent  stator  teeth,  through  the  corresponding 
gap  into  the  rotor  teeth  at  the  S  end,  and  thence  into  the  central 
core  again.  As  the  rotor  is  made  to  revolve,  the  teeth  are  alter- 
nately in  line  with  the  armature  coils  then  opposite  the  spaces 
between  coils.  The  flux  through  the  coils  consequently  pulsates, 
and  alternating  emfs.  are  induced. 

So  far  as  the  diagram  of  connections  is  concerned,  Fig.  123  applies 
to  this  case  quite  as  well  as  to  the  preceding  one,  for  the  shunt 
motor  and  generator  field  are  supplied  with  direct  current  in  either 
event,  and  alternating  current  flows  from  the  alternator  armature, 
whether  that  be  revolving  or  stationary. 

Self  Excited  Inductor  Alternator. — A  very  novel  construction  has 
lately  been  worked  out  for  fan  drive  on  airplanes.  A  simplified  dia- 
gram of  it  is  given  in  Fig.  125,  from  which  the  electrical  and  mag- 
netic circuits  may  be  traced,  and  the  principle  of  its  operation  may 
be  followed.  For  the  moment,  ignore  the  windings  on  the  rotor. 
The  machine  is  then  seen  to  be  an  inductor  alternator.  The  a.c. 
winding  is  on  the  16  stator  teeth,  each  tooth  and  its  adjacent  slot 
spanning  1/24  of  the  circumference.  These  teeth,  in  groups  of  4. 
form  four  polar  projections. 

The  polar  projections  are  made  to  have  opposite  polarities  around 
the  stator,  so  that  there  are  two  N  and  two  S  poles,  by  means  of  direct 
current  sent  through  the  field  coils  F,  each  of  which  consist  of  a  large 
number  of  turns.  The  field  coils  are  all  connected  in  series  to  the 
source  of  direct  current,  to  be  mentioned  hereafter,  but  the  connect- 
tions  are  omitted  from  the  sketch  to  avoid  having  so  many  lines. 

When  the  rotor  is  made  to  revolve,  the  flux  through  the  stator 
teeth  pulsates,  and  alternating  emfs.  are  induced  in  the  coils  encir- 


160  RADIO    COMMUNICATION. 

cling  them.  By  symmetry,  whatever  happens  in  any  one  coil  is  also 
going  on  at  the  same  time  in  eleven  others.  The  passage  of  the  in- 
ductor across  a  pair  of  consecutive,  oppositely  wound  teeth  gives 
rise  to  one  cycle.  The  generator  here  represented  is  intended  for 


FlG.JZB 


FIG.  125.— Self-excited  inductor  type  alternator.  (4.500  r.  p.  m.;  75  volts;  5  amp.. 
900  cycles  per  second.)  A,  terminals  of  a.  c.  winding;  B,  brushes  for  taking  d.  c; 
from  commutator;  C,  commutator  segments;  F,  d.  c.  field  coils;  J,  inductors; 
T,  stator  teeth. 

operation  at  4500  r.p.m.  and  at  that  speed,  with  the  12  inductors  as 
shown,  gives  a  frequency  of  900  cycles  per  second. 

Besides  having  on  it  the  inductors  for  the  alternator,  the  rotor  also 
functions  as  a  d.c.  armature.     That  accounts  for  the  windings  shown 


RADIO   COMMUNICATION.  161 

on  the  rotor.  How  such  an  armature  generates  direct  currents  is 
explained  in  Section  87.  For  present  purposes  it  suffices  to  say  that 
the  armature  consists  of  a  large  number  of  turns,  wound  of  course  for 
four  poles;  each  turn  spans  three  teeth.  In  the  diagram  the  con- 
nections have  been  simplified  for  purposes  of  illustration,  and  the 
number  of  commutator  segments  shown  is  much  smaller  than  on  the 
actual  machine.  Connections  not  shown  in  the  figure,  are  made 
between  the  field  coils  and  the  four  brushes,  two  positive  and  two 
negative.  The  brushes  are  shown  in  the  diagram  on  the  inside  of  the 
commutator,  for  clearness;  actually  they  are  on  the  outside.  The 
direct  current  from  this  armature  is  what  energizes  the  field  coils. 

It  will  thus  be  seen  that  the  rotor  serves  two  entirely  distinct 
purposes: 

1.  It  carries  the  inductors  for  the  a.c.  generator,  which  has  sta- 
tionary field  and  armature  coils. 

2.  It  carries  the  d.c.  armature  which  corresponds  to  the  exciter  in 
other  machines. 

95.  Radio  Frequency  Generators.  Alexanderson  High.  Frequency 
Alternator. — Frequencies  as  high  as  100,000  cycles  per  second  have 
been  secured  by  a  special  form  of  alternator 1  of  the  in  ductor  type .  It 
can  be  seen  at  once  that  100,000  inductor  teeth  have  to  pass  a  given 
point  every  second.  This  extraordinary  number  can  be  obtained 
only  by  having  a  great  many  teeth  on  the  rotor  and  driving  it  at  an 
unusually  high  velocity  besides.  In  a  2-kw.  generator,  the  rotor  has 
300  inductors  and  makes  20,000  r.p.m.  which  gives  the  required 
6,000,000  inductors  per  minute.  With  a  rotor  about  30  cm.  (1  ft.) 
in  diameter  this  allows  0.3  cm.  (|  in.)  for  each  slot  and  tooth  to- 
gether, and  even  then  the  rim  travels  something  like  19  km.  (12 
miles)  a  minute.  The  armature  conductors  are  laid  zigzag  in  little 
slots  in  the  flat  face  of  the  core,  this  face  being  perpendicular  to 
the  shaft.  (See  Fig.  126.) 

The  rotor  consists  of  a  steel  disk  with  a  thin  rim  and  much  thicker 
hub,  shaped  for  maximum  strength.  Instead  of  having  teeth  on  the 
edge,  it  is  slotted  with  little  windows,  the  inductors  in  the  form  of 
spokes,  and  leaving  a  solid  rim  of  steel.  Then  to  cut  down  the  air 

i  Developed  by  E.  F.  W.  Alexanderson,  of  the  General  Electric  Co.,  U.  S.  Pats. 
1,008,577;  1,110,028.  Description  of  several  models  is  given  in  Goldsmith's  Radio 
Telephony,  beginning  at  p.  117.  See  also  G.  E.  Review,  vol.  16,  p.  16  (1913). 

97340°— 19 11 


1G2 


RADIO    COMMUNICATION. 


friction,  the  slots  are  filled  with  non-magnetic  material  such  as  phos- 
phor-bronze, finished  off  smoothly  with  the  face  of  the  disk.  These 
machines  embody  a  number  of  novel  features  made  necessary  by  the 
small  space  per  inductor  and  the  exceptional  speed.  Their  construc- 
tion became  possible  only  through  engineering  skill  of  a  very  high 
order  and  by  fine  workmanship.  They  are  not  suitable  for  field 


Wind)  n£»  .scherne   o^    AleAAnderaon    Alternator 
i>-^lots    in  roTor 


-SfeTbr 


Circuits     of 
Cjoldschmidt   AlterrtAtor 


use,  however,  and  for  that  reason  a  detailed  description  is  not  given 
here. 

Goldsckmidt  Alternator. — A  principle  not  previously  mentioned  in 
connection  with  electrical  machinery  is  utilized  in  the  generators 
of  certain  high  power  German  stations.  Advantage  is  taken  of  the 
building  up  of  large  currents  by  electrical  resonance  (see  Sec.  109)  in 


RADIO   COMMUNICATION.  163 

the  rotor  and  stator  circuits  of  the  machine  itself,  as  well  as  of  the 
multiplication  of  frequency  by  the  effect  of  rotor  currents  on  the 
stator  windings.1 

Without  undertaking  to  give  the  proof  here,  it  may  be  stated 
that  when  a  rotor  is  revolved,  and  at  the  same  time  alternating 
currents  are  made  to  flow  at  a  frequency  corresponding  to  the  speed 
of  rotation  and  to  the  number  of  poles,  then,  due  to  these  currents, 
pulsations  take  place  in  the  strength  of  the  magnetic  field  of  the 
machine  at  double  the  frequency  of  the  alternating  currents. 

The  circuits  (in  simplified  form)  are  shown  in  Fig.  127.  Imagine 
S  to  be  the  stator  winding,  energized  by  some  source  of  direct 
current,  such  as  a  battery,  B.  In  the  magnetic  field  due  to  the 
stator  there  is  revolved  a  rotor,  represented  by  the  coil  R.  Suppose 
it  is  revolved  at  such  a  speed  that  the  alternating  emf .  induced  in  R 
has  a  frequency  of  10,000  cycles  per  second.  By  way  of  the  slip 
rin^s  this  emf.  is  impressed  on  the  circuit  C3L2C4,  which  is  tuned 
(Section  110),  so  that,  when  the  inductance  of  R  is  taken  into  ac- 
count the  natural  frequency  is  the  same  as  that  of  the  emf.  Then 
heavy  currents  will  flow  in  the  rotor. 

According  to  the  statement  made  above,  pulsations  will  take 
place  in  the  magnetic  flux  at  the  rate  of  20,000  per  second.  These 
will  induce  a  20,000-cycle  emf.  in  S.  If  the  inductances  and  capaci- 
tances SC^L^-2  are  chosen  for  resonance  at  that  frequency,  large 
currents  will  flow  in  the  stator  at  the  same  time  with  the  steady 
current  from  the  battery.  These  high  frequency  currents  are  pre- 
vented from  flowing  through  the  battery  by  the  high  inductance  L. 

The  20,000-cycle  stator  currents  cause  a  20,000-cycle  pulsation 
of  the  magnetic  flux  in  which  the  rotor  revolves,  and  when  the  rotor 
revolves  in  this  pulsating  field  it  gives  rise  to  a  triple  frequency  emf. ; 
that  is,  30,000  per  second  in  the  illustration  chosen.  The  con- 
denser C5  has  such  a  capacitance  that  the  circuit  #C3C5  resonates  to 
that  frequency,  and  the  30,000-cycle  currents  in  the  rotor,  in  view 
of  the  rate  of  rotation  of  the  latter,  cause  a  40,000-cycle  pulsation  of 
magnetic  flux  with  respect  to  the  stator  windings.  That  in  turn 
induces  a  40,000-cycle  emf.  in  S.  Remembering  that  the  antenna  A 
and  the  ground  G  constitute  a  condenser  (see  Section  137),  which 

i  The  following  brief  description  of  the  Goldsehmidt  alternator  is  based  on  a  fuller 
one  in  Goldsmith's  Radio  Telephony,  pp.  103-103,  where  further  information  may  be 
found.  See  also  C.  74,  p.  224. 


164  RADIO    COMMUNICATION. 

has  the  same  relation  to  the  stator  circuit  that  C5  has  to  the  rotor 
circuit,  it  is  seen  that  by  proper  tuning  the  circuit  SC-^AG  can  be 
made  to  resonate  at  the  final  frequency. 

Thus  by  providing  suitable  circuits,  it  is  possible  to  get  a  fre- 
quency four  times  as  great  as  that  corresponding  to  the  actual  speed 
and  number  of  poles  of  the  machine. 

The  principle  has  been  explained  as  though  the  machines  were 
bipolar.  Clearly,  that  would  necessitate  extraordinary  speeds. 
Instead,  the  large  generators  used  in  transatlantic  service  have 
360  poles  and  are  driven  at  4000  r.p.m.  by  250-h.p.  motors.  The 
fundamental  frequency  is  therefore  12,000,  which  is  quadrupled 
as  has  just  been  explained,  giving  48,000  at  the  antenna.  To  secure 
satisfactory  operation  the  finest  sort  of  workmanship  is  necessary 
in  building  them. 

E.  Motors. 

96.  Uses  of  D.C.  and  A.C.  Motors. — It  has  already  been  notedthat 
an  electric  motor  is  almost  identical  with  a  generator  in  structure, 
but  its  function  is  reversed;   it  converts  electrical  power  into  me- 
chanical power.     It  is  important  to  have  the  motor  suited  to  the 
kind  of  circuit  on  which  it  is  to  be  used;  a.c.,  or  d.c.,  the  right 
voltage,  etc.     Common  voltages  are  110  to  120;  220  to  240;  500  to  550; 
also,  for  a.c.,  440.     Lower  voltages  are   used  on  battery  circuits. 
A.c.  motors,  like  generators,  may  be  single  phase,  two  phase,  three 
phase,  etc.;  and  d.c.  motors  may  have  series,  shunt,  or  compound 
excitation. 

97.  D.C.  Shunt  Motor. — If  a  shunt  generator  is  used  for  charging 
a  storage  battery  and  the  engine  is  shut  off,  the  generator  will  con- 
tinue running,  provided  the  battery  is  large  enough,  but  an  ammeter 
in  the  circuit  shows  that  the  current  has  reversed.    The  battery  is 
discharging  and  the  generator  is  running  as  a  motor.     The  action 
is  explained  by  the  fact  that  when  a  current  is  sent  through  a  con- 
ductor in  a  magnetic  field,  there  is  a  force  that  tends  to  push  the 
conductor  across  the  field  (see  Section  43).     The  left  hand  rule  gives 
the  directions. 

Consider  the  simple  loop  in  Fig.  128,  between  the  poles  NS  of  an 
electromagnet.  If  the  wires  +  and  —  are  connected  to  a  source  of 
direct  current,  the  iron  will  be  magnetized.  At  the  same  time 
current  flowing  in  the  direction  of  the  arrows  in  the  loop  causes  a 


RADIO  COMMUNICATION. 


165 


force  toward  the  front  in  the  conductor  near  the  N  pole  and  a  force 
toward  the  back  in  the  conductor  near  the  S  pole.  The  loop  turns. 
The  effect  of  the  commutator  is  to  make  the  rotation  continuous, 
by  making  the  proper  connection  to  the  conductors  as  they  come 
into  place. 

By  a  line  of  reasoning  very  much  like  that  for  the  d.c.  generator, 
we  can  pass  from  this  simple  case  to  that  of  a  four-pole  drum- wound 
motor  illustrated  in  Fig.  129.  The  directions  of  current  and 
rotation  are  shown  by  arrows. 

Limiting  Speed. — It  might  be  expected  that  a  shunt  motor  would 
speed  up  indefinitely,  but  actually  it  soon  comes  to  a  definite  speed, 


FlQ.  It6 

Principle     of 
Motor 


and  then  continues  to  turn  so  fast,  but  no  faster.  As  soon  as  the 
armature  begins  to  rotate,  it  generates  an  emf.  according  to  the 
right  hand  rule.  This  action  is  exactly  the  same  as  in  a  generator. 
The  emf.  generated  is  opposite  to  the  direction  of  current  shown 
by  the  arrows,  and  is  for  that  reason  called  a  "counter  electromotive 
force."  The  faster  the  armature  turns,  the  greater  the  counter 
emf.  becomes.  It  cannot  turn  so  fast  that  the  counter  emf.  is  as 
great  as  the  line  voltage,  because  then  the  two  would  balance, 
there  would  be  nothing  to  make  the  current  flow  through  the  arma- 
ture, and  consequently  no  pull  to  keep  it  turning.  For  example, 


166 


RADIO    COMMUNICATION. 


suppose  the  armature  resistance  of  a  certain  motor  is  0.25  ohm, 
and  suppose  that  a  current  of  4  amp.  in  the  armature  furnishes  just 
enough  pull  to  keep  it  rotating.  If  the  speed  is  high  enough  to 
make  the  counter  emf.  109  volts  when  the  line  voltage  is  110,  the 
current  is  4  amp.1 


FIG.  129.— Diagram  of  circuits  of  a  4-pole  shunt  motor. 

Next,  suppose  the  motor  is  driving  machinery  that  calls  for 
five  times  as  great  a  pull.  The  speed  falls  off  a  little.  When  it  has 
fallen  enough  to  make  the  counter  emf.  105  volts,  the  current  is  20 


=         E  =  110-109  =  1  volt.    £=  0.25  ohm.    /  = 


0.25: 


4  amp. 


RADIO   COMMUNICATION.  167 

amp.1  If  that  is  enough  to  drive  the  load,  the  speed  will  be  steady 
at  the  new  rate.  So  by  changing  its  speed  a  very  little,  the  motor 
automatically  takes  more  or  less  current,  but  always  just  enough 
to  drive  its  load. 

The  magnets  are  always  of  the  same  strength,  regardless  of  load, 
because  the  current  around  them  depends  only  on  the  line  volts 
and  the  resistance  of  the  field  coils.  It  is  entirely  independent  of 
the  current  in  the  armature. 

Comparison  of  Generator  and  Motor  Actions. — In  both  generator 
and  motor  we  have  an  emf.  developed  in  the  armature  by  rotation 
in  a  magnetic  field.  Also,  in  both  we  have  currents  which  cause  a 
pull  on  the  armature  conductors.  If  the  machine  is  to  act  as  a 
generator,  its  armature  must  be  driven  at  such  a  speed  that  its  emf. 
is  higher  than  the  voltage  at  its  terminals,  due  to  emfs.  in  other 
parts  of  the  circuit.  Then  current  flows  with  the  emf.  This  cur- 
rent causes  a  back-drag  on  the  armature  and  makes  it  harder  to 
turn.  If  the  machine  acts  as  a  motor,  its  emf.  is  lower  than  that  of 
the  circuit  to  which  it  is  connected.  The  current  flows  against  this 
motor  emf.,  now  called  a  counter  emf.,  and  causes  a  forward  pull 
on  the  armature  which  keeps  it  turning. 

Starting  Box. — The  resistance  of  a  motor  armature  is  small.  The 
counter  emf.  developed  by  rotation  is  what  keeps  the  current  from 
becoming  excessive.  When  the  motor  is  first  connected  to  the 
line,  it  is  not  rotating  and  there  is  no  counter  emf.  Some  other 
way  must  be  found  to  keep  the  current  moderate.  The  simplest 
way  is  to  put  resistance  in  series  with  the  armature,2  and  then 
gradually  reduce  it  ("cut  it  out")  as  the  armature  gains  speed. 
The  resistance  is  usually  in  the  form  of  wires  or  grids,  mounted  in  a 
ventilated  iron  box,  the  whole  known  as  a  "starting  rheostat"  or 
"starting  box."  Various  forms  are  used;  Fig.  130  shows  the  con- 
nections in  one  type.  The  parts  drawn  in  solid  lines  are  supported 
on  an  insulating  face  plate,  commonly  slate.  The  internal  connec- 
tions are  drawn  in  dashed  lines.  Fig.  131  shows  how  the  starting 
box  is  connected  between  the  fused  main  switch  and  the  motor. 

When  the  resistance  is  all  cut  out,  the  iron  strip  K  comes  against 
the  electromagnet  M,  and  the  handle  is  held  in  place.  If  the  switch 

1  E  =  110-105  =  5  volts.    R  =  0.25  ohm.   /  =  Q-^  =  20  amp. 

2  The  field  excitation  is  not  cut  down,  but  is  of  full  strength  from  the  start. 


168 


RADIO    COMMUNICATION. 


(Fig.  131)  is  opened,  or  the  line  becomes  "dead"  for  any  other 
reason,  the  magnet  ceases  to  hold  K,  and  a  spring  S  (Fig.  130)  pulls 
the  handle  back  against  the  buffer  B,  thus  protecting  the  motor 
against  injury  in  case  the  current  is  turned  on  again. 


bo  A  -for  ohunt  motor 

L-  Connection  To  line      F-  Connection  to  .shunt"  -field 
&  -  Connection  To  Armature. 


Switch 


L  F  A 

m 


box 


F  i  q. 


shunt 
rnofor 


Connectiorvs    o^f  ahun"f  motor  and  starting  box 


Some  starting  boxes  have  four  terminals.  The  internal  connec- 
tions of  one  box  of  that  kind  are  shown  in  Fig.  132,  and  the  con- 
nections to  the  motor  in  Fig.  133.  The  extra  terminal  is  marked 
L— .  It  is  needed  because  the  electromagnet  for  the  "no  voltage 


RADIO   COMMUNICATION. 


169 


release  "  is  connected  directly  across  the  line,  the  high  resistance  Z, 
being  contained  in  the  box  to  keep  the  current  for  it  small. 

Connections  to  a  starting  box  must  be  made  according  to  the  way 
the  terminals  are  marked  on  the  box.     They  are  almost  always 


Lf 


FlQ.^Z 


Starting   box  with  two  "line"  terminals 
L"'",  L~,  .li'ne  "termmeifs  F— Connection  to  -shunt  field 

A  —  Connection  to  armature 


^      *     owircn          j_4-    L- 


Fia. 


moto 


Oonnecti'ons    ^or  o  ^hont  motor  and  sTArtin^ 
>opt    with  two  line    Termi'nals 


bo* 


stamped  with  letters  or  with  the  words  "line/'  "field,"  "armature," 
but  will  not  always  be  found  at  the  places  shown  in  Figs.  130 
and  132. 


170 


RADIO    COMMTJN ICATIOX . 


At  the  motor  the  circuits  are  often  brought  out  on  a  terminal 
board  after  the  fashion  of  Fig.  134.  Care  must  be  taken  not  to  get 
them  confused,  for  example,  by  connecting  the  field  in  place  of  the 
armature,  or  by  making  the  sort  of  mistake  shown  in  the  right  hand 
diagram  (marked  "wrong")  of  Fig.  134,  where  the  "-4"  terminal 
of  the  starting  box  is  wrongly  connected  to  the  junction  of  armature 
and  field,  and  the  " — Line"  is  wrongly  connected  to  the  armature 
alone.  Wrong  connections  are  bound  to  cause  trouble. 

Starting  and  Stopping.— The  proper  operations  for  starting  are: 

1.  See  that  handle  of  starting  box  is  in  the  "off"  position. 

2.  Close  switch  (see  Figs.  131,  133). 

3.  Move  starting  handle  to  first  contact.     Armature  should  begin 
to  turn.     If  it  fails,  open  the  switch  at  once,  for  something  is  wrong — 


Fid.  154 


Right 
£.l<5htand  wror^  connection-?  at  motor 


perhaps  a  faulty  connection,  loose  contact,  blown  fuse,  excessive 
overload,  wrong  brush  position,  etc. 

4.  As  armature  gains  speed,  move  handle  over  contacts,  one  step 
at  a  time.  Move  slowly  if  load  is  great,  taking  if  necessary  as  much 
as  30  seconds.  When  the  load  is  slight  and  the  motor  small,  a  few 
seconds  may  suffice. 

The  operation  for  stopping  is:  Open  main  switch.  In  a  few  sec- 
onds the  handle  should  snap  back  sharply.  If  it  fails,  move  it  back 
by  hand  and  look  for  dirty  contacts.  Sometimes  wiping  the  contact 
studs  and  putting  on  just  a  trace  of  vaseline  will  cure  the  trouble. 

Very  small  motors,  rated  at  a  fraction  of  a  horsepower,  are  often 
connected  directly  to  the  line  without  a  starting  rheostat  by  simply 
closing  a  switch. 

Reversing  Direction. — In  the  diagram  (Fig.  134)  the  mains  are 
marked  +  and  — .  As  a  matter  of  fact,  it  makes  no  practical  differ- 


RADIO  COMMUNICATION.  171 

ence  if  the  one  marked  +  is  really  — ,  and  vice  versa.  The  motor  runs 
in  the  same  direction.  It  can  be  reversed  by  taking  off  the  two 
connections  at  F  (left  hand  diagram.  Fig.  134)  and  interchanging 
them.  Care  must  be  taken  that  the  brushes  rest  on  the  commutator 
at  the  right  place  and  point  the  right  way  for  smooth  running,  as 
described  in  Section  106. 

Speed  Regulation  and  Control. — For  reasons  given  under  the  head- 
ing ''  Limiting  speed  "  a  shunt  motor  generally  runs  a  little 
more  slowly  when  loaded  (driving  machinery)  than  when  running 
free.  The  change  of  speed  is  called  the  "speed  regulation."  For 
most  motors  the  regulation  is  good,  the  change  in  speed  between  no 
load  and  full  load  being  only  5  per  cent  or  less.  Shunt  motors  are 
therefore  often  called  "constant  speed"  motors. 

This  supposes  that  the  voltage  applied  to  the  motor  is  constant. 
If  it  is  too  low,  the  speed  falls  off,  as  well  as  the  power  which  the 
motor  can  develop.  If  it  is  too  high,  the  motor  will  overspeed  some- 
what and  is  likely  to  overheat  and  to  spark  injuriously  at  the  com- 
mutator. The  speed  can  be  changed,  if  necessary,  by  several 
methods.  Only  two  will  be  described. 

A  resistance  in  series  with  the  armature  circuit  only  (not  the  joint 
line  to  armature  and  field)  will  reduce  the  speed.  The  conductor 
must  be  large  enough  to  carry  the  armature  current  without  over- 
heating. The  ordinary  starting  rheostat  will  not  serve,  as  it  is  not 
made  large  enough  for  continuous  duty.  It  would  quickly  overheat. 
Sometimes  special  rheostats  are  provided  for  starting,  which  are 
large  enough  to  be  left  in  circuit  continuously.  They  are  then 
usually  marked  "Regulating  rheostat,  for  continuous  duty." 

The  objection  to  this  scheme  is  that  it  wastes  power  and  that,  if 
the  load  changes,  the  speed  changes  too.  It  has  the  advantage  of 
being  simple. 

A  resistance  in  series  with  the  shunt  field  winding  increases  the 
speed.  This  seems  contradictory.  The  explanation  is  that  when 
the  field  current  is  reduced,  the  magnetism  is  weakened.  The  con- 
ductors have  to  move  faster  to  generate  about  the  same  counter  emf . 
as  before,  and  since  this  counter  emf.  is  always  nearly  as  great  as  the 
applied  voltage  the  speed  has  to  increase. 

The  objection  to  this  method  is  that  the  motor  may  overspeed  and 
burst  the  armature  by  centrifugal  force  if  too  much  resistance  is  used 
in  the  field  circuit.  There  is  also  danger  of  damaging  the  commuta- 
tor by  sparking.  It  is  not  wise  to  raise  the  speed  more  than  10  or 


172  RADIO    COMMUNICATION. 

15  per  cent  above  that  marked  on  the  name  plate  unless  the 
operator  is  very  sure  no  harm  will  follow. 

98.  D.C.  Series  Motor. — The  field  coils  of  a  motor  may  be  made  of 
thick  wire  and  connected  in  series  with  the  armature,  so  that  the 
same  current  flows  through  both.  It  is  then  called  a  "series" 
motor.  The  difference  in  connections,  compared  with  a  shunt 
motor,  is  the  same  as  for  the  corresponding  kinds  of  generator.  (See 
Pig.  117.)  Series  motors  differ  in  their  behavior  from  shunt  motors 
in  two  important  ways.  They  do  not  operate  at  constant  speed,  but 
run  very  much  more  slowly  when  heavily  loaded;  and,  at  the  lower 
speeds  they  develop  a  large  turning  force.  They  are  therefore  used 
on  street  cars,  for  cranking  gasoline  engines  on  automobiles,  and 
similar  duty  where  high  turning  effort  is  wanted  for  starting  a  load. 

Suppose  there  is  some  current,  say,  5  amp.,  flowing  in  armature 
and  field  coils.  Now  imagine  the  load  to  increase  until  the  current 
is  10  amp.  Two  things  happen.  If  the  magnetism  remained  the 
same,  the  doubled  armature  current  would  cause  double  the  pull. 
But  the  magnetism  does  not  remain  constant.  When  the  current 
doubles,  the  field  magnetism  increases,  because  the  10  amp.  flow  in 
the  field  coils  as  well  as  in  the  armature.  Thus  the  doubling  of  the 
armature  current  and  the  increased  magnetization  combined  make 
the  pull  much  more  than  double.  Also  the  stronger  field  would 
make  the  counter  emf.  automatically  increase  if  the  speed  remained 
unchanged.  But  this  is  impossible  because  the  counter  emf.  must 
always  be  a  little  less  than  the  line  voltage,  else  no  current  will  flow 
to  keep  the  motor  going,  so  the  speed  must  fall  off. 

The  turning  force  mentioned  above  is  called  "torque".  From 
the  explanation  just  given,  the  torque  of  a  series  motor  at  starting 
is  seen  to  be  great,  because  at  starting  the  speed  is  low  and  the 
armature  current  large.  The  less  the  load,  the  higher  the  speed. 
If  the  driving  belt  slips  off,  a  series  motor,  unless  it  is  quite  small, 
can  overspeed  enough  to  wreck  itself.  Series- motors  are  therefore 
direct  connected  or  geared  to  the  driven  machinery.  Shunt 
motors,  on  the  contrary,  will  not  over-speed  and  belts  may  safely 
be  used. 

Speed  Control. — The  only  way  of  controlling  the  speed  of  a  series 
motor  that  need  be  mentioned  here  is  by  using  a  rheostat.  Except 
for  small  motors,  one  is  needed  anyway  for  starting.  If  large  enough 
it  can  be  left  in  circuit  to  keep  down  the  speed.  Of  course  this  is 
wasteful,  because  the  heat  produced  in  the  rheostat  uses  electrical 
power. 


RADIO  COMMUNICATION.  173 

99.  Other  B.C.   Motors. — Connected   like    compound   generators 
(Fig.  117),  compound  motors  are  used  for  special  purposes,  but 
the  worker  with  radio  equipment  is  not  likely  to  run  across  them 
and  for  that  reason  they  are  not  treated  here.  l 

100.  Combination  A.  C.  andD.  C.  Motors. — Reversing  the  current 
in  the  line  to  which  a  series  motor  is  connected  has  no  effect  on 
the  direction  in  which  the  armature  turns.     If  the   current  is 
reversed  in  the  field  coils  alone,  the  magnetism  is  reversed,  and 
the  armature  turns  the  opposite  way.     Reversing  the   current  in 
the  armature  too,  makes  a  second  reversal  of   force,  that  is,  the 
armature  turns  as  it  did  at  the  beginning.     This  is  still  true  when 
the  reversals  are  so  rapid  that  the  current  is  truly  alternating,  so 
the  same  motor  can  be  used  for  a.c.  and  d.c.     But  in  that  case 
some  special  construction  is  necessary;  for  example,  the  magnets 
are  built  up  of  laminations,  instead  of  being  in  a  solid  piece. 

101.  Induction   Motors. — When   the   terminals  of   any   coil  are 
connected  to  a  circuit,  the  current  sets  up  a  magnetic  field  in  and 
around  the  coil.     When  a  number  of  coils  are  arranged  in  the  form 
of  a  stationary  two-phase  or  three-phase  armature  2  and  connected 
to  a  corresponding  two-phase  or  three-phase  power  circuit,  there 
comes  the  remarkable  result,  that  the  alternating  currents,  flowing 
in  the  coils,  produce,  inside  of  the  armature,  a  magnetic  field  which 
rapidly  and  continuously  revolves.     The  iron  core  and  the  copper 
coils  are  both  stationary;  only  the  magnetism  changes.     If  the 
changes  of  current  are  made  slowly,  a  compass  needle  placed  in 
the  open  space  within  the  armature  will  spin  just  as  if  it  were 
directed  by  an  imaginary  magnet  with  its  poles  sliding  along  the 
face  of  the  armature. 

Next,  let  an  iron  core  with  suitable  coils  on  it  be  placed  inside 
this  armature,  on  a  shaft,  so  that  it  can  turn.  The  revolving  magnetic 
field  cuts  across  the  conductors  of  this  movable  ''rotor";  that  sets 
up  emfs. ;  currents  flow,  and  now  we  have  conductors  with  currents 
in  them  in  a  magnetic  field.  Consequently  the  rotor  begins  to  turn. 
It  speeds  up  until  it  turns  nearly  as  fast  as  the  moving  magnetic 
field.  How  fast  that  is  depends  on  the  construction  of  the  station- 
ary armature,  and  the  frequency  (cycles  per  second)  of  the  alter- 
nating current  supplied. 

1  Compound  motors  are  explained  in  Rowland,  p.  126;   Franklin  and  Estey,  Dyna- 
mos and  Motors,  p.  144;  Timbie,  p.  221. 

2  See  Fig.  101. 


174  RADIO   COMMUNICATION. 

The  machine  just  described  is  an  "induction"  motor.  l  Its 
parts  are  called  the  stator  (stationary  part)  and  rotor  (part  that  re- 
volves) just  as  in  an  alternator.  Nothing  has  been  said  about  any 
connection  between  the  rotor  and  an  external  electric  circuit.  In 
the  simplest  form  of  induction  motor  there  is  no  such  connection. 
The  rotor  is  dragged  around  magnetically  at  a  practically  constant 
speed.  A  pulley  on  the  rotor  shaft  can  be  used  with  a  belt  to 
deliver  power  to  some  other  machine. 

In  some  forms  of  induction  motor  there  are  connections  between 
the  rotor,  which  in  that  case  has  slip  rings,  and  an  external  circuit. 
But  the  external  circuit  is  not  a  power  circuit;  it  merely  consists 
of  resistances  for  controlling  the  motor  speed. 

The  terms  "squirrel  cage"  and  "wound"  are  often  used  to 
describe  rotors;  the  first  means  the  simple  kind  with  conductors 
of  plain  bars  of  metal  and  no  slip  rings  or  other  moving  contacts; 
the  second  means  the  kind  having  coils  like  an  armature,  and, 
commonly,  slip  rings. 

If  one  of  the  connections  to  a  three-phase  induction  motor  is 
opened,  leaving  only  two  attached,  the  rotor  continues  to  turn. 
Two  wires  can  supply  only  a  simple  a.c.  (single  phase),  so  it  is 
evident  that  an  induction  motor  can  be  used  on  a  single  phase 
circuit.  But  it  will  not  start  on  a  single  phase  without  a  special 
starter. 

Like  d.c.  motors,  those  for  a.c.  have  to  be  operated  at  about 
the  voltage  for  which  they  were  built.  In  addition,  they  have 
to  be  connected  to  a  line  of  the  right  frequency.  Then  they  run 
at  certain  definite  speeds,  which  are  nearly  as  high  at  full  load 
as  when  running  free.  On  60-cycle  circuits,  the  common  speeds 
for  small  motors  are  a  little  under  1800,  1200,  and  900  r.p.m. 

Starting. — Small  induction  motors  are  started  by  simply  connecting 
them  to  the  right  kind  of  power  circuit  by  a  switch,  double-pole  (two 
blades,  for  two  wires)  for  single  phase,  three-pole  for  three-phase,  and 
four-pole  for  two-phase  motors.  With  polyphase  (two  or  three- 
phase)  motors,  this  produces  the  revolving  magnetic  field  as  pre- 
viously explained.  With  single  phase,  the  action  is  different.  It 
was  said,  earlier  in  this  section,  that  an  induction  motor  will  not 
start  on  one  phase,  but  will  continue  if  started  somehow.  One  way 

i  For  further  explanation  of  action  see  Timbie  and  Higbie,  A.C.  Machinery, 
Second  Course,  pp.  429-449;  Franklin  and  Estey,  Dynamos  and  Motors,  pp.  340-362 
Rowland,  pp.  252-270. 


RADIO   COMMUNICATION.  175 

might  be  to  give  it  a  start  by  hand.  Generally  that  is  not  a  practical 
method.  A  second  way  is  to  use  a  '  'phase  splitter.  "  That  merely 
means  that  the  current  goes  through  the  stator  by  two  paths  in 
parallel,  one  having  more  inductance  or  capacitance  than  the  other. 
Inductance  in  any  branch  of  a  circuit  causes  a  phase-lag  in  that 
branch.  The  armature  must  have  two  sets  of  coils,  and  if  the  cur- 
rents in  them  differ  as  to  phase,  the  motor  starts  as  a  sort  of  two- 
phase  machine.  After  it  gets  up  to  speed,  one  winding  (the  '  'start- 
ing" winding)  is  disconnected.  That  may  be  done  by  hand,  a 
special  two-way  switch  being  provided  with  a  starting  and  a  running 
position  or  there  may  be  an  automatic  centrifugal  cut  out  in  the 
motor.1 

A  third  way  is  by  ' 'repulsion  motor"  action.  Then  the  rotor  has 
a  commutator  and  brushes,  like  those  for  d.c.  The  stator  is  con- 
nected to  the  supply  line,  the  rotor  is  not.  The  brushes  are  con- 
nected together  by  a  short  circuiting  conductor.  When  currents 
flow  in  the  stator,  other  currrents  are  induced  in  the  rotor2  and  it 
begins  to  turn.  At  the  proper  speed,  a  centrifugal  device  short- 
circuits  the  commutator  and  so  converts  the  machine  into  a  simple 
induction  motor.  At  the  same  time,  the  brushes  are  lifted  automati- 
cally, to  reduce  friction. 

Larger  three-phase  motors  are  started  by  applying  a  fraction  of  full 
voltage,  obtained  by  a  combined  transformer  and  double-throw 
switch  known  as  a  '  'compensator.  "  3 

F.  Motor-Generators  and  Dynamotors. 

102.  Motor-Generators.— When  electric  current  is  to  be  had,  but 
not  in  the  form  needed,  the  change  is  made  by  transformers,4  recti- 
fiers, motor-generators  or  dynamotors,  according  to  circumstances. 
The  first  named,  change  a.c.  at  one  voltage  to  another  voltage  at  the 
same  frequency.  The  second,  change  a.c.  to  pulsating  d.c.  The 
last  two  are  used  for  changing  a.c.  at  one  frequency  to  a.c.  at  another 
frequency  or  to  steady  d.c.,  or  the  reverse;  also  for  changing  d.c. 
from  one  voltage  to  another. 

i  Split  phase  starting  is  described  in  Timbie  and  Higbie,  A.C.  Electricity,  Second 
Course,  pp.  510-512. 

*  See  Timbie  and  Higbie,  A.C.  Electricity,  Second  Course,  p.  514;  Rowland,  p.  270; 
Franklin  and  Estey,  pp.  383,  386;  Standard  Handbook,  p.  542. 

»  For  details,  and  other  methods  of  starting,  see  Timbie  and  Higbie,  A.C.  Electric., 
p.  454;  Franklin  and  Estey,  Dynamos  and  Motors,  p.  360;  Standard  Handbook, 
pp.  520, 1292, 1293. 

«  Described  in  Sec.  62. 


176  RADIO    COMMUNICATION. 

The  most  easily  understood  way  to  make  the  change  is  by  the  use 
of  a  suitable  combination  of  motor  and  generator,  built  for  the  same 
speed  and  mounted  on  a  common  base,  the  shafts  being  coupled 
together.  Such  a  combination  is  a  '  'motor-generator. " 

Motors  and  generators  have  been  described.  The  combination 
brings  no  new  ideas.  Each  part  can  be  thought  of  by  itself,  without 
regard  to  the  other.  Examples  of  such  machines  have  been  given.1 
In  radio  practice  they  are  used  particularly  for  battery  charging  and 
for  supplying  spark  and  arc  circuits. 

Battery  Charging. — Motor-generators  for  battery  charging  are  used 
where  the  supply  is  a.c.  or  d  c.  at  the  wrong  voltage.  In  the  latter 
case  if  the  d.c.  voltage  is  too  high,  a  rheostat  may  be  used,  but  it 
wastes  power.  When  several  low  voltage  batteries  have  to  be 
charged,  they  may  be  connected  in  series  and  the  power  wasted  in 
resistance  thereby  reduced. 

The  generator  of  a  battery  charging  unit  is  usually  shunt- wound. 
The  voltage  of  a  storage  battery  rises  as  it  gets  charged.  Also,  at  the 
beginning  it  is  allowable  to  use  a  larger  current  than  toward  the  end 
of  the  charge.  The  voltage  of  a  shunt  generator  is  lower  when  it  is 
delivering  a  large  current  than  when  the  current  is  small.2  There- 
fore such  a  generator,  connected  to  a  discharged  battery  and  given 
the  proper  setting,  produces  a  large  current  which  gradually  de- 
creases as  the  battery  voltage  rises.  It  is  also  possible  to  use  a  com- 
pound generator,  so  designed  that  the  voltage  is  substantially  con- 
stant, whatever  the  current,  within  the  limits  of  the  machine.  In 
that  case  the  initial  rate  of  charging  the  battery  is  higher  than  when 
a  shunt  generator  is  used,  but  falls  off  in  the  same  way.  A  high  rate 
of  charging  at  the  beginning  cuts  down  the  time  required  for  the 
whole  process,  and  is  therefore  desirable,  provided  it  does  not  injure 
the  battery.  Modern  portable  batteries  will  stand  charging  in  this 
way  and  compound  generators  may  consequently  be  used.  The 
proper  treatment  for  a  given  battery  must  be  learned  from  instruc- 
tions pertaining  to  that  particular  form. 

Motor -generators  are  used  also  for  connection  to  ordinary  lighting 
circuits  (about  110  volts)  to  get  500  or  600  volts  d.c.  for  arc  trans- 
mitters,3 or  for  connection  to  such  circuits  or  to  low  voltage  storage 
batteries  to  get  a.c.  at  500  to  900  cycles  for  use  with  transformers  in 
audio  frequency  spark  transmitters.4  Such  apparatus  has  been 
described  in  Section  94. 

i  Sec.  94,  Figs.  121,  122,  124.  s  See  Sec.  174. 

a  Shown  in  Fig.  118.  *  See  Sec.  154. 


RADIO  COMMUNICATION.  177 

103.  Rotary  Converters. — If  connections  are  made  to  a  pair  of 
collector  rings  from  opposite  sides  of  a  two-pole  d.c.  armature,  it  will 
generate  alternating  current.     At  the  same  time,  direct  current  can 
be  taken  from  the  commutator.     In   that   case   the  machine  is  a 
"double  current  generator."     If  not  driven  by  an  engine,  but  con- 
nected to  a  d.c.  circuit,  it  operates  as  a  shunt  motor  and  can  be  used 
to  generate  a.c.     Operated  on  a.c.  as  a  motor,  it  delivers  d.c.     When 
used  for  such  conversion,  it  is  called  a  rotary  converter.     When  an 
a.c.  generator  is  used  as  a  motor  (not  an  induction  motor)  it  requires 
d.c.  for  field  excitation  and  operates  at  the  exact  speed  (called' 
"synchronous  "  speed),  corresponding  to  the  frequency  of  the  supply. 
The  d.c.  for  the  rotary  converter  field  comes  from  the  commutator. 
On  the  other  hand,  when  such  a  converter  is  used  to  generate  a.c., 
the  frequency  depends  on  the  speed  of  rotation  of  the  armature, 
which  can  be  controlled  as  previously  described  for  the  shunt  motor. 

The  rotary  converter  has  the  advantage  of  accomplishing  in  a 
single  machine  what  the  motor-generator  does  in  two.  Its  dis- 
advantage is  that  the  voltage  at  the  generator  end  depends  entirely 
on  the  voltage  supplied  to  it  as  a  motor,  the  a.c.  voltage  in  the  case 
of  a  single  phase  converter  being  about  71  per  cent  of  the  d.c.  voltage, 
slightly  more  or  less  depending  on  the  direction  of  the  conversion. 
Thus,  if  operated  on  a  10- volt  storage  battery,  it  would  give  about  7 
volts  a.c.  Also,  frequencies  anything  like  500  cycles,  which  it  is 
desirable  to  get  in  radio  communication  from  d.c.  with  storage  bat- 
teries as  a  source,  are  impossible;  either  the  speed  or  the  number  of 
commutator  segments  would  have  to  be  increased  beyond  reason. 

Instead  of  single  phase,  rotary  converters  can  be  built  for  two- 
phase  or  three-phase  currents,  the  former  by  four  connections  equally 
spaced  on  the  armature  and  four  rings,  the  latter  by  three  connections 
and  three  collector  rings.  The  statements  made  for  bipolar  machines 
are  equally  true  for  multipolar  rotary  converters,  if  it  is  understood 
that  each  ring  has  as  many  connections  to  the  armature  as  there  are 
pairs  of  poles. 

104.  Dynamotors. — Rotary  converters  cannot  be  used  for  changing 
direct  current  at  one  voltage  to  d.c.  at  another  voltage.     The  most 
compact  machine  for  that  purpose  is  the  "dynamotor."     An  appli- 
cation which  will  occur  to  the  radio  student  is  the  securing  of  several 
hundred  volts  for  the  plate  potential  of  vacuum  transmitting  tubes 

97340°— 19 12 


178 


RADIO    COMMUNICATION. 


from  batteries  giving  only  10  or  12  volts.  (See  Fig.  135.)  In  the 
dynamotor  two  separate  armature  windings  are  placed  on  a  com- 
mon core.  One  acts  as  a  motor,  the  other  as  a  generator.  There  is 
but  one  frame  and  one  set  of  field  magnets.  The  two  windings  are 
connected  to  commutators  at  opposite  ends  of  the  shaft.  The  ratio 
of  voltages  is  fixed  when  the  machine  is  built,  so  the  output  voltage 


-I'l'l'l'l'l 

Dyn*motor    connections  for  conversion  from    lo  to  ioo  Volta 


Lew 

Voltage 


Dou  ble    current  ^enerATor 
for   low  *r>el  hi£h  voft&^e 


S-  3hunt  c.oil.3 

D-  Differential   coils 

R«      -  Automatic  ruUT 


depends  on  the  voltage  applied.  The  field  coils  receive  current 
from  the  same  source  as  the  motor  armature. 

105.  Double  Current  Generators. — A  dynamotor  can  be  driven 
by  mechanical  power  as  a  generator,  and  can  then  deliver  d.c.  at 
two  different  voltages.  Such  machines  have  been  designed  for  fan 
drive  on  airplanes,  the  low  and  high  voltages  being  used  for  the  fila- 
ment and  plate  currents,  respectively,  of  vacuum  tube  transmitters. 

To  get  constant  voltages,  in  spite  of  the  varying  speed  at  which 


RADIO  COMMUNICATION.  179 

the  armature  is  driven,  the  field  flux  must  be  weakened  as  the  speed 
rises.  Current  taken  from  one  commutator  is  sent  around  the  field 
coils,  supplying  the  main  magnetization.  A  weaker  current  from 
the  other  commutator  is  sent  around  the  opposite  way,  giving  a 
differential  effect.  (Fig.  136).  If  the  speed  rises,  and  consequently 
the  voltage,  the  current  in  the  second  winding  is  made  to  increase 
considerably  by  a  sensitive  automatic  regulator.  The  flux  is  there- 
fore reduced,  counteracting  the  effect  of  the  rise  in  speed. 

106.  Common  Troubles. — Electrical  machinery  is  subject  to  the 
same  troubles  as  other  machinery,  such  as  rough,  gritty,  dry  or  tight 
bearings,  bad  alignment,  sprung  shaft,  etc.,  which  show  themselves 
by  heating,  taking  excessive  power,  and  vibration.  The  bearings 
must  be  clean  and  smooth.  Care  must  be  taken  never  to  spring  or 
jam  the  shaft.  There  must  always  be  enough  oil  of  good  quality  in 
the  oil  wells  to  keep  the  bearings  thoroughly  lubricated.  Most 
generators  and  motors  are  oiled  by  means  of  brass  rings  that  ride  on 
the  shaft  and  dip  into  the  oil  and  carry  it  up  as  they  turn.  Some- 
times these  are  injured  in  taking  the  machine  apart;  then  they  do 
not  turn  properly;  the  bearing  runs  dry  and  heats. 

Some  machines  have  ball  bearings.  They  should  run  very  easily, 
but  are  subject  to  the  same  troubles  as  a  bicycle  bearing,  such  as 
broken  balls,  grit,  adjustment  too  tight.  In  general  if  a  bearing 
gets  too  hot  to  be  borne  with  the  hand,  it  needs  attention;  the 
trouble  is  likely  to  grow  worse,  until  finally  the  shaft  binds  firmly 
and  cannot  be  turned.  The  job  of  getting  it  free  again  may  then  be 
a  very  tedious  and  troublesome  one. 

Another  point  of  friction  is  at  the  brushes.  If  they  are  pressed  in 
too  firmly,  they  rub  harder  than  necessary.  They  should  be  fitted 
smoothly  so  as  to  give  the  full  area  of  electrical  contact,  then  exces- 
sive pressure  will  not  be  needed.  They  should  be  only  tight  enough 
to  make  good  contact  and  prevent  sparking  or  flashing.  When 
carbon  brushes  are  working  properly,  the  metal  surface  on  which 
they  rub  becomes  finely  polished,  and  wears  down  very  slowly. 
This  is  particularly  noticeable  in  the  case  of  copper  commutators 
on  direct  current  machines. 

Besides  those  of  a  mechanical  nature  there  may  be  electrical 
troubles,  some  requiring  expert  attention,  others  easily  found  and 
cured.  The  most  common  electrical  troubles  are  caused  by  loose, 
wrong  or  missing  connections,  and  dirt. 


180  RADIO    COMMUNICATION. 

Connections  (usually  accidental)  that  allow  current  to  pass  by  a 
piece  of  apparatus,  instead  of  flowing  through  it,  are  called  "short 
circuits."  They  are  a  common  source  of  trouble. 

A  systematic  way  of  hunting  troubles  is  as  follows: 

1.  Make  or  find  a  circuit  diagram,  unless  thoroughly  familiar 
with  the  connections  and  positive  they  are  right.     In  drawing  dia- 
grams follow  each  branch  of  the  circuit  from  the  source  (-(-terminal 
of  battery  or  generator  armature)  completely  around  (through  the 
—  terminal)  to  the  place  of  beginning.     Remember  that  no  current 
will  flow  in  a  circuit  or  in  any  part  of  a  circuit  unless  there  is  a 
difference  of  potential  in  it. 

2.  Trace  the  wiring  according  to  the  diagram. 

3.  While  tracing,  see  that — 

(a)  Fuses  are  good,  if  any  are  in  circuit. 
(6)  Connections  are  clean  and  good. 

(c)  Contact  is  not  prevented  by  insulating  caps  of  binding  screws 
or  insulation  of  wire. 

(d)  Wires  do  not  touch,  making  short  circuits. 

(e)  There  are  no  extra  wires  or  connections. 

(/)  There  are  no  breaks  in  wire  inside  of  the  insulation.  This 
occasionally  happens  with  old  lamp  cord.  The  broken  place  is 
very  limber,  and  can  be  pulled  in  two  more  readily  than  a  sound 
place. 

4.  Look  for  defects  in  the  apparatus  itself. 

In  a  generator,  besides  loose  connections,  electrical  troubles  easily 
remedied  are,  for  d.c. : 

5.  Failure  to  generate  emf . ,  caused  by — 

(a)  Brushes  not  in  the  right  place.  On  nearly  all  d.c.  generators 
of  reasonably  modern  construction,  the  proper  position  for  the 
brushes  on  the  commutator  is  nearly  opposite  the  middle  of  the 
field  poles,  or  slightly  forward  (in  the  direction  of  rotation)  of  that 
point.  The  exact  location,  found  by  trial,  is  that  which  gives 
sparkless  commutation.  Brushes  are  set  right  at  the  factory,  and 
should  be  left  as  they  are,  unless  there  is  good  reason  to  believe  that 
they  have  since  been  shifted. 

(6)  Brushes  not  making  good  contact  because  of  bad  fit  or  too  little 
pressure.  Test  by  lifting  them  slightly,  one  by  one,  to  detect  loose 
springs;  also  try  pressing  brushes  to  commutator  with  dry  stick. 
Remedy  by  working  fine  sandpaper  back  and  forth,  sharp  side  out, 


RADIO  COMMUNICATION.  181 

between  commutator  and  brush  (holding  it  in  such  a  way  that  the 
toe  of  the  brush  is  not  ground  off)  or  by  tightening  brush  springs,  as 
needed. 

Brushes  are  designed,  either  to  press  against  the  commutator 
squarely,  pointing  toward  the  center  of  the  shaft,  or,  more  commonly, 
to  trail  somewhat  as  an  ordinary  paint  brush  might  trail  if  held 
against  the  commutator.  However,  there  is  also  in  very  satisfactory 
use  a  form  of  holder  by  which  the  brushes  are  held  pointing  against 
the  direction  of  rotation.  Instead  of  sliding  up  or  down  in  a  box 
they  are  pressed  against  a  smooth  face  of  brass  by  springs. 

(c)  Field  connections  reversed. 

6.  Sparking,  when  caused  by 

(a)  Roughened  commutator;  cured  by  holding  fine  sandpaper 
(not  emery)  against  it  while  running. 

(6)  Brushes  shifted;  for  remedy  see  5,  above.  It  is  very  impor- 
tant that  all  brushes  be  at  the  proper  points.  This  means,  for 
example,  that  if  the  brushes  are  supposed  to  touch  at  four  points, 
spaced  a  quarter  way  around  the  commutator,  they  shall, actually  be 
exactly  a  quarter  of  a  circumference  apart,  as  tested  by  fine  marks 
on  a  strip  of  paper  held  against  the  commutator. 

7.  Heating  of  commutator  due  to  brush  friction.     Reduce  tension 
of  springs. 

In  a.c.  generators  look  for — 

8.  Loose  connections  and  bad  contacts  at  brushes.     Position  of 
brushes  on  rings  is  immaterial,  as  there  is  no  commutation. 

In  d.c.  shunt  motors,  motor-generators,  or  dynamotors,  the  simple 
troubles  are: 

9.  Failure   to  start,   or  starting  suddenly   with  speed   quickly 
becoming  excessive,  due  to  wrong  connections.     See  Section  97. 

10.  Sparking,  caused  by  excessive  load  or  wrong  brush  position. 
See  5  and  6  above.      The  proper  position  for  motor  brushes  is 
slightly  backward,  (against  the  direction  of  rotation)  of  the  center 
of  the  field  poles. 


CHAPTER  3. 

RADIO  CIRCUITS. 
A.  Simple  Radio  Circuits. 

107.  The  Simplicity  of  Radio  Theory.— The  principles  of  alter- 
nating currents  developed  in  Chapter  1  are  applicable  to  radio  cir- 
cuits. Radio  currents  are  merely  very  high  frequency  alternating 
currents.  The  fundamental  ideas  of  sine  waves  (Section  50)  apply  to 
what  are  known  as  continuous  or  "undamped  waves."  " Damped 
waves"  also  behave  in  many  ways  like  sine  waves;  for  some  purposes 
slight  modifications  of  the  sine  wave  theory  are  needed.  These  are 
treated  in  Part  13  below. 

The  frequencies  of  alternation  of  radio  currents  are  very  high. 
Ordinary  alternating  current  power  circuits  use  frequencies  from 
25  to  60  cycles  per  second.  The  lowest  radio  frequencies,  however, 
lie  above  some  20,000  cycles  per  second,  and  the  upper  limit  may 
be  put  at  perhaps  10,000,000  cycles  per  second.  Such  an  enormous 
difference  in  frequency  should  naturally  give  rise  to  some  differences 
in  the  behavior  of  radio  circuits  as  distinguished  from  low  frequency 
alternating  current  circuits. 

In  low  frequency  a.c.  circuits  the  principal  opposition  to  the 
current  is  offered  by  the  resistance.  The  inductive  reactance  and 
capacitive  reactance  are  far  greater  than  the  resistance  in  a  radio  cir- 
cuit,  and  resistance  plays  only  a  minor  role.  The  reactance  of  such 
email  inductances  as  are  provided  by  a  few  turns  of  wire  is  of  im- 
portance, and  condensers  whose  small  capacitance  would  very 
effectually  prevent  the  flow  of  ordinary  alternating  currents  readily 
allow  the  passage  of  radio  currents.  The  mutual  inductance  effect 
of  one  circuit  on  another  is  much  greater,  when  radio  frequencies 
are  used,  than  is  the  case  with  ordinary  alternating  current  circuits. 
The  enormous  frequencies  used  in  radio  work  give  rise  also  to  much 
larger  skin  effect,  eddy  currents,  and  dielectric  losses  than  would 
be  the  case  if  the  same  circuit  were  worked  at  low  frequency. 

Furthermore,  measuring  instruments  commonly  used  for  alter- 
nating current  work  are,  for  the  most  part,  unsuitable  for  use  in 
182 


RADIO   COMMUNICATION. 


183 


radio  circuits,  or  require  modified  methods  of  connection.  Instru- 
ments whose  indications  depend  upon  the  heating  effect  (Section  59) 
are,  in  general,  suitable  for  radio  work.  Direct  current  instruments 
may  also  be  used  but  in  connection  with  rectifying  devices.  The 
telephone  receiver,  so  useful  in  low  frequency  work,  requires  a 
rectifier  also.  At  low  frequencies,  the  diaphragm  of  the  receiver 
vibrates  with  the  current,  giving  an  audible  singing  note  of  the  same 
frequency  as  the  alternating  current.  Radio  currents  execute  their 
changes,  however,  altogether  too  quickly  to  be  followed  by  the 
telephone  directly,  and  even  were  it  possible  for  the  diaphragm  to 
vibrate  so  rapidly,  the  sound  produced  would  be  of  too  high  pitch 
to  be  heard  by  the  ear.  It  is  found  to  be  necessary,  therefore,  to 
break  up  the  radio  currents  into  groups  of  rectified  waves.  Each 


—  1 

Pi  a.  ivr 

} 

c 

O 

L 

g 

Simple    Seriea    Circuit 

g 

E. 

1 

group  gives  a  single  impulse  to  the  diaphragm,  and  if  the  impulses 
follow  regularly  with  sufficient  rapidity  a  musical  note  is  produced. 

108.  The  Simple  Series  Circuit. — The  simplest  form  of  radio  cir- 
cuit is  one  having  resistance,  inductance,  and  capacitance  in  series, 
as  in  Fig.  137.  An  alternating  emf.  is  supposed  to  be  applied  at  E. 

In  Chapter  1,  Section  57,  it  has  been  shown  that  the  value  of  the 
current  produced  in  a  circuit,  to  which  an  alternating  emf.  is  ap- 
plied, may  be  calculated  by  the  equation, 

emf. 


Current1 


"impedance. 


If  the  effective  value  of  the  emf.  is  used  here,  the  equation  gives 
the  effective  value  of  the  current.  (Sec.  51.) 

The  impedance  Z  depends  not  only  on  the  resistance  R,  but  on 
the  reactance  X  of  the  circuit  as  well.  (Sees.  55,  57.)  For  a  sine 
wave  of  applied  emf. 

(69) 


184 


RADIO   COMMUNICATION. 


That  is,  the  square  of  the  impedance  is  found  by  adding  the 
squares  of  the  resistance  and  the  reactance.  The  impedance  can 
therefore  never  be  less  than  the  resistance,  and  may  be  very  much 
greater.  If  the  resistance  in  the  circuit  is  very  small  in  comparison 
with  the  reactance,  the  impedance  is  practically  equal  to  the 
reactance.  The  impedance  is  measured  in  ohms. 

As  has  been  pointed  out  (Sec.  49),  the  reactance  is  the  opposition 
offered  to  the  current  by  an  inductance  or  a  capacitance.  The 
reactance  of  an  inductance  coil  is  equal  to  2-n-  times  the  frequency, 
times  the  inductance.  For  a  capacitance  the  reactance  is  equal  to 

2vfC  ^ec.  56),  in  which  /  is  the  frequency  and  C  is  the  capaci- 
tance. In  their  reactive  effects  an  inductance  and  a  capacitance 
tend  to  offset  one  another,  so  that  the  total  reactance  of  an  inductive 
ceil  and  a  condenser  in  series  is  found  by  taking  the  difference  of 
their  individual  reactances. 

Example. — Let  us  calculate  the  reactance  of  the  combination  of  a 
coil  of  500  microhenries  inductance  in  series  with  a  condenser  of 
0.005  mfd.  capacitance  at  several  different  frequencies. 


Frequency 
cycles  per 

Reactance  of 
coil 

Reactance  of 
condenser 

Total  react- 
ance 

second. 

(ohms). 

(ohms). 

(ohms). 

60 

0.188 

-530,000 

-530,000 

1.000 

3.142 

-31,  840 

-31,837 

100,000 

314.2 

-318.4 

—4.2 

100,  700 

316.23 

-316.  23     |                     0 

1,000,000 

3,142 

-31.84               -3,110 

The  table  shows  at  a  glance  that  the  reactance  of  the  coil  is  small 
at  low  frequencies,  increases  as  the  frequency  rises,  and  becomes 
very  considerable  at  the  higher  frequencies,  such  as  occur  in  radio 
work. 

The  behavior  of  the  condenser  is  just  the  reverse.  At  the  lowest 
frequency  it  offers  a  very  large  reactance,  but  at  radio  frequencies 
the  impedance  is  vastly  smaller.  For  very  high  frequencies  the 
reactance  would  be  negligible. 

In  most  radio  circuits  the  resistance  of  the  circuit  can  be  kept  as 
small  as  a  few  ohms.  It  is  therefore  obvious  that  only  in  the  case 
of  the  100,000  cycles,  in  the  table,  would  it  be  necessary  to  take 
account  of  the  resistance  in  calculating  the  impedance. 


RADIO    COMMUNICATION.  185 

For  example,  if  R=5  ohms,  the  impedance  for  the  frequencies  in 
the  table  above,  will  have  the  values  530,000,  31,837,  6.5,  5  and 
3110,  respectively.  In  all  except  the  third  and  fourth  cases,  the 
difference  between  the  reactance  and  the  impedance  is  less  than 
one  part  in  a  million  of  the  total. 

It  is  thus  apparent  that  in  many  cases  the  impedance  of  a  circuit 
depends  almost  entirely  on  the  reactance  of  the  circuit.  Only  in 
those  cases  where  the  reactance  is  small  is  it  necessary  to  take  the 
resistance  into  account. 

109.  Series  Resonance. — It  would  seem  at  first  sight,  then,  that 
radio  circuits  would  offer  for  the  most  part  a  high  impedance  and 
that  therefore  very  little  current  could  flow,  except  with  very 
large  emf .  This  is  in  general  true  of  any  radio  circuit  if  the  fre- 
quency be  taken  at  random.  However,  by  properly  adjusting  the 
value  of  the  frequency,  the  reactance  of  the  circuit  may  be  made 
zero.  This  is  at  once  evident,  when  we  remember  that  the  inductive 
reactance  increases  with  the  frequency,  while  the  capacitive  react- 
ance diminishes.  At  some  definite  frequency,  then,  the  inductive 
reactance  of  the  coil  must  have  the  same  value  as  the  capacitive 
reactance  of  the  condenser,  and  since  they  act  against  each  other, 
the  total  reactance  will  be  zero. 

This  may  be  shown  graphically.  In  Fig.  138  are  plotted  the 
curves  A  and  B  of  the  reactances  of  the  coil  and  condenser,  respec- 
tively, of  the  previous  example.  Frequencies  are  measured  along 
the  horizontal  axis  and  reactances  along  the  vertical  axis.  The  react- 
ances of  curve  B  are  taken  as  negative  to  distinguish  between  the 
opposing  effects  of  the  inductive  and  capacitive  reactances.  Curve 
Cia  obtained  by  taking  the  algebraic  sum  of  the  reactances  of  curves 
A  and  B.  It  is  the  curve  of  resultant  reactance  in  the  circuit.  For 
the  particular  values  of  C  and  L  chosen  in  this  example,  the  circuit 
acts  like  an  inductive  reactance  at  all  frequencies  greater  than  a 
value  of  slightly  above  100,  000  cycles,  while  below  that  point  it  has 
the  character  of  a  capacitive  reactance.  Furthermore  for  only  a 
narrow  range  of  frequencies,  99,000  to  103,000,  perhaps,  the  reactance 
of  the  circuit  is  less  than  10  ohms.  For  most  frequencies  the  react- 
ance is  much  greater  than  this. 

The  frequency  which  makes  the  capacitive  and  inductive  react- 
ances equal  is  called  the  "resonance  frequency"  of  the  circuit,  and 
the  circuit  is  said  to  be  in  "resonance,"  or  to  be  "tuned"  to  the 
frequency  in  question.  It  is  important  to  be  able  to  calculate  the 


Variation   of 
reactance  with 
the  Frequency 
L- So  ©microhenries 
C-o  ocS^mfd. 


Corves  -fo 
Series  Ci'rcuit   with 
Different   Resistances 


Resis>"fence  on  the 
of  Reaondnee  Curve 


186 


RADIO    COMMUNICATION.  187 

frequency  for  resonance.     To  do  so,  the  condition  must  be  fulfilled, 
that 


(70) 

which  shows  that  the  frequency  at  resonance  must  be 

1 


Applying  this  relation  to  the  example  under  discussion,  and  sub- 
stituting therein  L =0.0005  henry,  C=5/109  farad,  the  resonance 
frequency  is  found  to  about  100,700  cycles  per  second.  The  react- 
ances of  both  the  coil  and  the  condenser  at  this  frequency  are  the 
same  and  have  the  value  316.2  ohms.  This  value  may,  of  course, 
be  calculated  by  using  for/  the  value  of  the  resonance  frequency  in 

either  of  the  expressions  2-n-fL  or  0    fn-     It  is  of  interest  to  note 

^jTTy  O 

that  each  of  these  expressions  for  reactance  reduces  simply  to  -• /— » 

when  the  frequency  has  the  resonance  value. 

There  exists,  then,  for  any  series  circuit  containing  inductance 
and  capacitance,  a  definite  value  of  the  frequency,  for  which  the 
total  reactance  in  the  circuit  is  zero,  and  the  impedance  is  simply 
equal  to  the  resistance  of  the  circuit.  This  frequency  is  called  the 
resonance  frequency,  and  the  circuit  is  said  to  be  in  a  condition  of 
resonance.  The  impedance  has  its  smallest  value,  and  the  current 
which  flows  in  the  circuit  when  the  applied  emf.  has  any  value 
whatever  has  the  largest  value  possible  with  that  value  of  fre- 
quency. 

These  facts  may  be  readily  verified  experimentally  by  inserting 
in  a  simple  radio  circuit  a  suitable  ammeter  for  measuring  the  cur- 
rent. If  now  the  frequency  of  the  applied  emf.  is  gradually  raised, 
the  current  will  at  first  be  small  and  will  increase  very  slowly  as  the 
frequency  is  increased.  In  the  immediate  neighborhood  of  the 
resonance  frequency,  the  current  will  suddenly  begin  to  increase 
rapidly,  for  small  changes  of  frequency,  and  after  passing  through 
a  maximum,  will  rapidly  decrease  again  as  the  frequency  is  raised 
to  still  higher  values.  The  results  of  such  an  experiment  may  be 
shown  by  a  curve  in  which  frequencies  are  measured  in  the  hori- 
zontal direction,  while  the  values  of  the  current  corresponding  are 


188  RADIO    COMMUNICATION. 

plotted  vertically.  Since  most  instruments  suitable  for  measuring 
radio  currents  give  deflections  proportional  to  the  square  of  the  cur- 
rent, it  is  customary  to  plot  the  squares  of  the  current,  or  the  deflec- 
tions of  the  instrument,  rather  than  the  current  itself.  Such  "reso- 
nance curves"  are  plotted  in  Fig.  139,  and  they  show  plainly  the 
"resonance  peak." 

On  account  of  its  great  importance  in  radio  work  the  phenomenon 
of  resonance  requires  further  study.  To  fix  our  ideas,  let  us  suppose 
that  a  circuit  whose  inductance  and  capacitance  have  the  values 
already  chosen  in  the  previous  example,  has  a  resistance  of  5  ohms 
and  that  an  emf .  of  10  volts  is  applied  in  the  circuit.  The  maximum 
possible  value  of  the  current  is  found  by  dividing  the  applied  voltage 
by  the  resistance,  which  gives  2  amp.  This  current  will  flow  when 
the  frequency  has  the  critical  value  of  100,700  cycles  per  second. 
To  study  the  distribution  of  emf.  over  the  different  parts  of  the  cir- 
cuit we  have  to  remember  (Sec.  55)  that  the  emf.  between  any  two 
points  of  the  circuit  has  to  have  a  value  equal  to  the  product  of  the 
current  by  the  impedance  between  the  two  points.  Accordingly 
the  emf.  between  the  ends  of  the  resistance  is  2X5=10  volts,  that  on 
the  coil  is  2X316.23=632.46  volts,  and  the  same  emf.  is  found 
between  the  terminals  of  the  condenser  also. 

The  existence  of  such  a  large  voltage  on  both  the  coil  and  the  con- 
denser explains  how  it  is  possible  to  obtain  such  a  relatively  large 
current  through  the  large  reactances  of  the  coil  and  condenser.  The 
small  applied  voltage  is  employed  only  in  keeping  the  current  flow- 
ing against  the  resistance  of  the  circuit,  not  for  driving  the  current 
through  the  coil  or  condenser.  To  explain  the  presence  of  the  large 
voltages  on  coil  and  condenser,  it  must  be  remembered,  as  was  shown 
in  Section  59,  that  when  a  current  is  flowing  through  an  inductance 
and  capacitance  in  series,  the  emf.  on  the  inductance  opposes  that  on 
the  capacitance  at  every  moment.  The  sum  of  the  voltages  on  the 
two  is  therefore  found  by  subtracting  their  individual  values. 
Since  at  the  resonance  frequency  the  emf.  on  the  inductance  has  the 
same  value  as  the  emf.  on  the  capacitance,  the  emf.  between  the 
terminals  of  the  two  in  series  is  therefore  zero. 

Energy  is  supplied  to  the  circuit  by  the  source  at  a  rate  which  may 
be  determined  (when  the  resonance  condition  has  been  established) 
by  simply  multiplying  the  emf.  by  the  current.  (Sec.  55.)  That  is, 
in  the  present  instance,  the  power  is  10X2=20  watts.  The  power 
dissipated  in  heat  in  the  resistance  may  be  calculated  by  taking  the 


RADIO    COMMUNICATION.  189 

product  of  the  resistance  by  the  square  of  the  current.  (Sec.  51.) 
In  this  case  it  is  5X22=20  watts.  The  source,  therefore,  supplies 
energy  to  the  circuit  at  just  the  right  rate  to  make  good  the  energy 
dissipated  in  heat  in  the  resistance.  After  the  current  has  reached 
the  final  effective  value  (2  amp.  in  this  case),  no  further  energy  is 
supplied  to  the  coil  or  condenser  by  the  source,  but  their  energy  is 
simply  transferred  back  and  forth,  from  one  to  the  other,  without  loss 
or  gain  in  the  total  amount,  nor  is  any  outside  agency  necessary  to 
maintain  this  condition. 

Mechanical  Example  of  Resonance. — Many  mechanical  examples  of 
resonance  might  be  cited.  It  is  a  well  known  fact  that  the  order  to 
" break  step"  is  often  given  to  a  company  of  soldiers  about  to  pass 
over  a  bridge.  Neglect  of  this  precaution  has  sometimes  resulted  in 
such  violent  vibrations  of  the  bridge  as  to  endanger  it.  This  is  espe- 
cially the  case  with  certain  short  suspension  bridges. 

When  a  shock  is  given  to  a  bridge  it  vibrates,  and  the  frequency  of 
the  vibrations,  that  is,  the  number  of  vibrations  per  second,  is 
always  the  same  for  the  same  bridge,  whatever  the  source  of  the 
shock.  The  frequency  of  vibration  is  analogous  to  the  resonance 
frequency  of  the  circuit.  For  if  an  impulse  be  applied  to  the  bridge 
at  regular  intervals,  tuned  so  that  the  number  of  impulses  per  second 
is  exactly  equal  to  the  number  of  vibrations  natural  to  the  bridge  in 
the  same  time,  violent  vibrations  may  be  set  up,  although  the  indi- 
vidual impulses  may  be  small.  In  fact,  when  the  bridge  is  thus 
vibrating,  the  impulses  need  to  have  only  just  force  enough  to  over- 
come the  frictional  forces  and  thus  keep  the  vibrations  from  dying 
away.  The  much  greater  forces  involved  in  the  vibrations  them- 
selves correspond  to  the  large  voltages  acting  on  the  coil  and  conden- 
ser. The  voltage  on  the  condenser  is  of  the  same  nature  as  the  large 
forces  which  exist  in  the  beams  of  the  bridge  when  they  are  stretched, 
while  the  voltage  on  the  coil  corresponds  to  the  very  considerable 
momentum  of  the  moving  bridge.  The  small  force  of  the  impulses 
given  the  bridge  corresponds  to  the  small  applied  emf.  in  the  elec- 
trical case. 

If  the  vibrations  of  the  bridge  ever  become  so  violent  as  to  rupture 
it,  it  means  that  the  beams  have  been  stretched  beyond  their  break- 
ing point.  Similarly,  the  dielectric  of  the  condenser  may  be 
broken  by  the  emf.  existing  between  its  terminals,  in  cases  where 
the  resonance  current  is  too  lar^e. 


190  RADIO    COMMUNICATION. 

110.  Tuning  the  Circuit  to  Resonance. — The  practical  importance 
of  resonance  lies  in  the  fact  that  it  enables  the  impedance  of  a 
circuit  to  be  made  equal  to  the  resistance  alone.  It  must  be 
remembered  that  the  reactance  of  the  small  inductances  in  the 
circuit,  which  are  unavoidable,  become  important  at  radio  fre- 
quencies and  may  often  be  much  greater  than  the  resistance. 

This  fact,  taken  in  connection  with  the  smallness  of  the  emf. 
of  incoming  signals,  would  make  it  impossible  to  obtain  any  but 
minute  currents  in  the  receiving  apparatus  with  inductance  alone 
in  the  circuit.  From  this  standpoint,  the  sole  function  of  the 
tuning  of  the  circuit  to  resonance  is  to  offset  the  inductive  react- 
ance by  an  equal  capacitive  reactance,  so  that  the  impedance  may 
be  made  as  small  as  the  resistance. 

The  circuit  may  be  tuned  to  resonance  in  three  ways — 

(a)  By  adjusting  the  frequency  of  the  applied  emf. 

(6)  By  varying  the  capacitance  in  the  circuit. 

(c)  By  varying  the  inductance  in  the  circuit. 

Of  these,  the  first  case  has  already  been  treated.  The  other 
two  find  application  in  receiving  circuits  where  the  frequency 
of  the  incoming  waves  is  beyond  the  control  of  the  operator  in  the 
use  of  coupled  circuits  and  in  the  adjustment  of  the  frequency  of 
the  waves  emitted  in  certain  methods  of  sending. 

The  possibility  of  tuning  a  circuit  is  of  course  not  confined  to 
radio  circuits,  but  is  present  also  with  ordinary  alternating  current 
circuits,  and  is  becoming  common  in  telephone  work.  However, 
at  low  frequencies  the  values  of  the  inductance  and  capacitance 
involved  are  relatively  great,  so  as  to  make  it  inconvenient  to  vary 
their  values  in  steps  sufficiently  small.  Furthermore,  in  low 
frequency  work  the  reactances  of  the  coils  likely  to  occur  in  the 
circuit  are  small,  and  the  large  quantities  of  power  involved  render 
the  use  of  condensers  relatively  uncommon.  The  inductances 
and  capacitances  used  in  radio  work,  on  the  other  hand,  are  rela- 
tively small,  and  the  construction  of  coils  of  continuously  variable 
inductance  (variometers  or  variable  inductors)  and  of  apparatus 
of  variable  capacitance  (variable  condensers)  offers  no  particular 
difficulties. 

From  formula  (71)  it  appears  that  it  is  the  product  of  the  induc- 
tance and  capacitance,  rather  than  their  actual  values,  which  de- 
termine the  resonance  frequency.  To  tune  a  circuit  to  a  given 
frequency,  the  inductance  may  be  large  or  small,  provided  only 


RADIO    COMMUNICATION.  191 

that  the  capacitance  may  be  so  adjusted  that  the  product  of  induc- 
tance and  capacitance  shall  have  the  value  corresponding  to  the 
frequency  assumed. 

111.  Resonance  Curves. — A  resonance  curve  is  a  curve  which 
shows  the  changes  of  current  in  a  circuit,  when  changes  are  made 
which  cause  the  resonance  condition  to  be  somewhat  departed  from. 
For  example,  the  current  (or  square  of  the  current)  may  be  plotted 
for  different  values  of  the  frequency  somewhat  above  or  below  the 
resonance  frequency.  Or,  the  curve  may  show  the  change  in 
current,  when  the  capacitance  (or  inductance)  is  somewhat  raised 
and  lowered  with  respect  to  the  value  which  holds  for  the  condition 
of  resonance.  Such  curves  are  often  determined  experimentally, 
in  whole  or  in  part,  on  account  of  their  value  in  calculating  the 
damping  of  the  circuit.  (Damping  is  treated  in  Sec.  116  below.) 
Such,  for  example,  are  the  curves  of  Fig.  139,  in  which  are  plot- 
ted the  values  of  the  current  squared,  to  some  arbitrary  scale,  for 
different  values  of  the  capacitance  of  the  variable  condenser.  The 
inductance  of  the  circuit  was  fixed  at  the  value  377  microhenries 
Three  different  curves  were  determined  with  the  resistance  in  the 
circuit  fixed  at  the  values  4.4,  9.4  and  14.4  ohms,  respectively. 

Sharpness  of  Resonance. — It  was  of  course  to  be  expected  that 
the  value  of  the  current  at  resonance  (height  of  the  peak),  should  be 
greater,  the  smaller  the  resistance  in  the  circuit,  but  attention  needs 
to  be  called  particularly  to  the  sharpness  of  the  curve  with  the 
smallest  resistance  and  to  the  flatness  of  the  curve  with  greatest  re- 
sistance. This  is  the  characteristic  of  resonance  curves  in  general, 
and  is  a  necessary  consequence  of  the  equations  for  the  impedance. 
It  may  be  shown  still  more  clearly,  if  the  scales  to  which  the  three 
curves  are  plotted  are  so  altered  that  the  peaks  of  the  three  curves 
have  the  same  height.  This  has  been  done  in  Fig.  140. 

The  same  results  may  be  seen  by  calculating  the  square  of  the  im- 
pedance with  different  settings  of  the  condenser  and  with  different 
resistances  in  the  circuit.  The  resonance  frequency  in  this  case  was 
169,100  cycles  per  second,  which  shows  that  with  the  inductance 
of  377  microhenries  the  setting  of  the  condenser  at  resonance  is  almost 
exactly  2350  mfd.  The  reactance  of  condenser  and  coil  at  this  fre- 
quency is  400.56  ohms  in  each  case. 

The  following  table  shows  the  impedances  for  three  different  set- 
tings of  the  condenser  when  the  resistance  of  the  circuit  has  the  three 
values  corresponding  to  those  of  the  curves.  The  squares  of  the  cur- 


192 


RADIO    COMMUNICATION. 


rents  are,  of  course,  less  in  proportion  as  the  squares  of  the  impedance 
are  greater. 


Setting  of 
condenser 
(micro-mfd). 

Impedance  squared. 

For  #=4.4 

For  72=9.4 

For  #=14.4 

2300 
2350 
2400 

94.1 
19.3 
90.0 

163.1 
88.3 
158.9 

282 
207 

278 

For  the  smallest  resistance,  the  square  of  the  current  is  about  4.7 
times  as  great  at  resonance  as  when  the  capacitance  is  changed  by 
50  micro-mfds.  in  either  direction.  For  9.4  ohms  in  circuit  the  ratio 
is  about  1.8,  and  for  the  largest  resistance,  only  about  1.35.  These 
calculated  ratios  agree  very  well  with  the  experimental  values. 
The  close  connection  of  the  shape  of  the  resonance  curve  with  its 
resistance,  points  to  the  possibility  of  calculating  the  total  resistance 
in  the  circuit  from  measurements  of  the  resonance  curve.  For  this 
method  of  measuring  radio  resistance  see  0.  74,  Sections  49  and  50. 

The  calculations  here  given,  as  well  as  an  inspection  of  the  curves  of 
Fig.  139,  show  that  the  resonance  curve  is  not  symmetrical.  That 
is,  the  current  has  not  the  same  value  when  the  capacitance  is  a  cer- 
tain amount  less  than  the  resonance  value,  that  it  has  when  the  value 
of  the  capacitance  is  greater  by  the  same  amount.  The  question  of 
this  lack  of  symmetry  is  treated  in  the  next  section. 

Symmetry  of  Resonance  Curves. — The  curves  of  Fig.  138  show  the 
changes  of  coil  reactance,  curve  A,  and  condenser  reactance,  curve 
B,  together  with  the  total  reactance,  curve  C  (their  sum)  when  the 
frequency  is  changed.  The  curve  of  total  reactance  is  not  symmetri- 
cal about  the  axis  where  it  passes  through  its  zero  value  (point  Z, 
Fig.  138).  The  resonance  peak  (Fig.  139)  is,  therefore,  unsymmetrical 
also.  That  is,  the  current  is  not  the  same  for  two  frequencies,  one 
slightly  higher  than  the  resonance  frequency,  and  the  other  the  same 
number  of  cycles  lower  than  the  resonance  frequency.  The  expla- 
nation is  found  in  the  shape  of  the  curve  of  condenser  reactance. 

The  same  lack  of  symmetry  exists  when  the  inductance  and  the  fre- 
quency are  held  constant  and  the  capacitance  is  varied  to  obtained 
resonance,  because  the  shape  of  the  curve  of  condenser  reactance  in 
this  case  is  the  same  as  in  the  preceding.  However,  if  the  frequency 
and  capacitance  are  held  constant,  and  the  resonance  condition  is 
reached  by  varying  the  inductance,  a  symmetrical  resonance  peak  is 


RADIO    COMMUNICATION. 


193 


obtained;  equal  changes  of  the  inductance,  above  and  below  the 
setting  for  resonance,  will  cause  the  current  to  fall  to  the  same  value. 
The  difference  of  this  case  from  the  two  preceding  lies  in  the  fact  that 
curves  of  condenser  and  coil  reactance  and  hence  of  total  reactance, 
are  here  straight  lines. 

To  summarize  then,  the  resonance  curve  is  symmetrical  when  the 
tuning  is  accomplished  by  varying  the  inductance  ( C  and/ constant), 
but  is  not  symmetrical  in  the  two  other  methods  of  tuning,  viz.,  by 
varying  the  capacitance  (L  and  /  constant)  or  by  varying  the  fre- 
quency (Cand  L  constant). 

112.  The  Wavemeter. — The  phenomenon  of  resonance  enables 
one  to  obtain  relatively  large  currents  in  a  circuit  to  which  only 


a  small  emf.  is  applied,  provided  only  that  the  circuit  is  properly 
tuned.  To  determine  when  the  condition  for  resonance  is  realized 
with  a  given  frequency  in  a  given  circuit,  or  to  measure  the  frequency 
at  which  a  circuit  of  predetermined  constants  should  be  in  resonance, 
use  is  made  of  the  "wavemeter."  This  is  the  most  important 
instrument  used  in  radio  measurements.  It  consists  essentially 
of  a  series  circuit,  which  includes  an  inductance  and  a  capacitance, 
both  of  which  are  of  known  values.  Either  the  inductance  or  the 
capacitance  may  be  of  fixed  value  while  the  other  will  be  variable. 
A  hot  wire  ammeter,  thermo-j unction,  or  other  suitable  device  for 
measuring  radio  currents  is  inserted,  either  directly  into  the  circuit 
(Fig.  141),  or,  better,  is  coupled  electromagnetically  to  it,  the  cou- 
97340°— 19 13 


194  RADIO    COMMUNICATION. 

pling  being  made  as  loose  (Sec.  119)  as  will  permit  of  a  suitable  max- 
imum deflection  of  the  ammeter  (Fig.  142). 

If  the  frequency  of  the  current  in  a  given  circuit  is  to  be  measured, 
the  coil  of  the  wavemeter  circuit  is  placed  near  the  circuit  in  ques- 
tion, and  the  capacitance  of  the  wavemeter  is  varied,  until  the 
indicating  device  shows  that  the  current  in  the  wavemeter  circuit 
is  a  maximum.  In  making  the  final  adjustment  the  wavemeter 
coil  should  be  moved  as  far  away  from  the  circuit  in  question  as 
is  possible  and  yet  provide  a  convenient  maximum  deflection  of  the 
current  indicating  device. 

From  the  known  value  L  of  inductance  of  the  wavemeter  coil 
and  the  capacitance  Cr,  corresponding  to  the  setting  of  the  con- 
denser at  resonance,  the  desired  frequency  may  be  calculated 
from  equation  (72)  which  gives 


What  is  generally  desired,  however,  is  not  so  much  the  frequency 
as  the  wave  length  (Sec.  124)  of  the  electromagnetic  waves  radiated 
by  the  circuit.  The  wave  length  X  is  connected  with  the  frequency 
/  by  the  fundamental  relation 

\=y  (73) 

in  which  c  is  the  velocity  of  electromagnetic  waves  in  space  and 
has  the  value  of  300,000,000  meters  per  second.  Expressing  Cr 
in  mfd.  and  L  in  microhenries,  as  is  commonly  convenient,  the 
fundamental  wavemeter  equation  giving  the  wave  length  in  meters 
is 

X=1884  T/LCT  (74) 

For  example,  if  £=1000  microhenries  and  Cr=0.001mfd.,  the  wave 
length  emitted  by  the  circuit  is  1884  meters. 

A  wavemeter  is  usually  provided  with  a  buzzer  or  some  other 
auxiliary  device  by  means  of  which  oscillations  may  be  set  up  in 
the  wavemeter  circuit.  These  will  have  a  wave  length  which 
may  be  calculated  by  equation  (74)  from  the  inductance  and  capaci- 
tance of  the  wavemeter  circuit.  By  coupling  any  desired  circuit 
with  the  wavemeter  circuit  an  emf.  is  introduced  into  the  former, 
when  the  buzzer  is  working,  the  frequency  of  which  is  the  same  as 
that  existing  in  the  wavemeter  circuit.  This  frequency  may  be 
calculated  by  (74)  from  the  known  inductance  of  the  wavemeter 


RADIO    COMMUNICATION.  195 

coil  and  the  capacitance  corresponding  to  the  setting  of  the  conden- 
ser. If,  further,  it  is  desired  to  tune  the  circuit  in  question  to  the 
frequency  emitted  by  the  wavemeter  circuit,  it  is  only  necessary 
to  couple  the  current  indicator  to  the  circuit  to  be  tuned,  to  cause 
the  wavemeter  to  emit  waves  and  to  vary  the  capacitance  or  induct- 
ance of  the  circuit  to  be  adjusted,  until  the  indicator  shows  a  maxi- 
mum current. 

113.  Parallel  Resonance. — In  the  preceding  sections  it  has  been 
shown  how  to  obtain  the  maximum  current  in  a  circuit  for  a  given 
applied  emf.  The  principle  of  resonance,  utilized  for  this  purpose, 
finds  application  also  in  the  solution  of  the  reverse  problem  of 
keeping  currents  of  a  certain  frequency  out  of  any  chosen  part  of  a 
circuit  without,  however,  preventing  the  passage  of  currents  of 
other  frequencies.  To  such  an  arrangement  is  given  the  appropriate 
name  of  a  " filter."  A  filter  consists  essentially  of  an  inductance 
coil,  joined  in  parallel  with  a  condenser.  This  combination  is 
interposed  between  the  emf.  in  question  and  that  portion  of  the 
circuit  from  which  the  undesirable  currents  are  to  be  excluded. 
Any  such  combination  of  inductance  and  capacitance,  taken  at 
random,  will  oppose  currents  of  a  single  frequency  only,  whose 
value  depends  principally  on  the  values  of  the  inductance  and 
capacitance.  To  render  such  an  arrangement  effective  against 
currents  of  a  certain  chosen  frequency,  it  is  necessary  to  adjust  the 
capacitance  and  inductance  to  have  a  definite  relation.  The  solu- 
tion of  this  problem  requires  a' knowledge  of  the  principles  of  "paral- 
lel resonance." 

Fig.  143  shows  a  coil  of  inductance  L  and  resistance  R,  joined 
in  parallel  with  a  condenser  of  capacitance  C.  The  current  /  flows 
from  the  alternating  source  of  emf.  E,  through  the  main  circuit, 
and  at  the  branch  point  divides,  a  part  I\  flowing  through  the  coil, 
and  the  remainder,  Ic  through  the  condenser.  At  every  moment, 
the  current  /  has  a  value  which  is  the  algebraic  sum  of  the  values 
of  TI  and  Ic  existing  at  that  same  moment.  Let  us  suppose,  first, 
that  the  emf.  E  has  a  definite  frequency,  and  that  the  inductance 
of  the  coil  is  invariable.  Current  measuring  instruments  may  be 
arranged  to  measure  the  three  currents.  If  the  capacitance  is  varied 
continuously,  and  the  indications  of  the  ammeters  recorded,  the 
following  experimental  facts  will  be  observed. 

In  general,  the  currents  in  the  coil  and  condenser  will  be  unequal, 
and  the  current  I  may  be  less  than  either.  As  the  capacitance  is 
varied,  the  currents  in  the  coil  and  condenser  may  be  made  to 


196 


RADIO    COMMUNICATION. 


approach  equality,  and  at  the  same  time  the  main  current  will 
decrease.  At  length,  for  some  critical  value  of  the  capacitance,  the 
main  current  will  reach  a  very  small  minimum  value,  while  the 
current  in  the  coil  and  the  condenser  current  are  nearly  equal. 
Further,  each  is  many  times  larger  than  the  main  current.  As  the 
capacitance  is  now  varied  still  further,  the  main  current  begins  to 
increase,  and  the  coil  and  condenser  currents  are  no  longer  so  nearly 
equal. 

As  an  example,  assume  the  inductance  of  a  coil  to  be  1000 
microhenries  and  its  resistance  2  ohms.  An  effective  emf.  of  10 
volts  and  a  frequency  of  71,340  cycles  per  second  is  applied.  (This 


I-  -175    microhenne 
o  micro  -mfd 


parallel   Resonance   Cur> 


Venation    of  A^^arenT  inductanc 
of  a  coil   wifh       wave   length 


value  of  frequency  was  chosen,  since  it  gives  a  minimum  current  /, 
with  a  condenser  of  almost  exactly  0.005  mfd.)  The  changes  of  the 
current  in  the  main  circuit,  as  the  capacitance  is  varied  from  0.002 
to  0.008  mfd.  are  shown  in  Fig.  144,  in  which  values  of  the  capaci- 
tance are  measured  horizontally  and  values  of  the  square  of  the 
current  vertically.  The  latter  values  in  the  figure  are  multiplied 
by  a  million.  The  minimum  current  is  not  zero,  but  its  value  is 
only  about  0.0001  amp.,  a  value  whose  square  is  too  small  to  be 
easily  distinguished  in  the  figure.  The  corresponding  currents  in 
the  coil  and  condenser  are  each  about  0.02236  amp.  Their  difference 


RADIO    COMMUNICATION.  197 

is  only  about  1/100,000  part  of  this  value,  the  condenser  current 
being  the  larger  by  this  minute  amount. 

In  practice,  then,  if  we  imagine  some  troublesome  emf.  to  be 
introduced  into  the  circuit  at  E  (Fig.  143),  by  induction  or  otherwise, 
the  employment  of  a  parallel  combination  of  inductance  and  capac- 
itance can  be  made  to  very  completely  prevent  this  emf.  from 
causing  currents  to  flow  in  the  circuit,  provided  only  that  the  values 
of  inductance  and  capacitance  are  properly  chosen.  And  such  a 
filter  does  not  prevent  the  passage  of  currents  of  other  frequencies. 

If,  for  example,  we  suppose  that  the  emf.  E  has  a  frequency  of 
100,000  cycles,  in  the  above  case  the  combination  of  1000  micro- 
henries and  0.005  mfd.  would  allow  0.01549  amp.  to  flow  in  the  main 
circuit.  That  is,  this  filter  has  155  times  as  much  stopping  effect  for 
currents  of  71,340  cycles  per  second  as  for  currents  of  100,000  cycles, 
and  for  frequencies  further  away  the  effect  would  be  greater.  Fil- 
ters of  this  kind  are  used  in  airplane  radio  telephone  sets  to  remove 
noises  produced  by  the  electric  generator  used  in  the  set;  for  example, 
in  the  type  SCR-68  sets.  A  similar  filter  is  used  in  connection  with 
the  type  EE-1  buzzerphone.1 

The  results  of  theory  show  that  to  filter  out  currents  of  a  frequency 
/,  the  necessary  relation  between  inductance  and  capacitance  is 
given  in  the  following  equation: 


(75) 


The  current  in  the  main  circuit  is,  under  this  condition, 


(76) 


In  all  practical  radio  circuits,  however,  the  resistance  of  a  circuit  is 
so  small  in  comparison  with  the  inductive  reactance,  that  it  may  be 
neglected.  The  equation  (75),  under  these  circumstances,  goes  over 
into  the  same  equation  that  holds  for  series  resonance,  that  is  — 


Otherwise  expressed,  then,  it  may  be  stated,  that  when  the  con- 
dition of  parallel  resonance  is  realized,  the  loop  circuit  which  con- 
tains the  coil  and  condenser  in  series  is  very  closely  in  a  condition 

i  See  S.  C.  Electrical  Engineering  Pamphlet  No.  1. 


198  RADIO    COMMUNICATION. 

of  series  resonance.  Recalling  the  fact  that,  in  the  series  resonance 
condition,  the  emf.  on  the  condenser  is  equal  and  opposite  to  that 
on  the  coil,  it  is  easy  to  see  that  there  is  here  a  flow  of  current  back 
and  forth  between  the  coil  and  condenser.  Viewed  from  the  main 
circuit  (Fig.  143),  the  current  in  the  coil  is,  at  every  moment,  oppo- 
site to  the  condenser  current,  so  that  the  main  current,  which  is  their 
algebraic  sum,  is  at  every  moment  merely  the  difference  between 
the  condenser  and  coil  currents.  These  latter  being  nearly  equal 
in  value,  we  have  the  explanation  of  the  existence  of  the  relatively 
large  currents  in  the  coil  and  condenser,  when  the  main  circuit  is 
almost  free  from  current. 

The  ideal  filter  would  be  one  in  which  the  resistances  of  the  in- 
ductance coil  and  all  the  connecting  wires  in  the  two  branch  circuits 
were  actually  zero.  In  such  a  case,  the  condition  for  parallel  reso- 
nance would  be  rigorously  the  same  as  for  series  resonance,  equation 
(70),  the  condenser  current  would  be  exactly  equal  to  the  current 
in  the  coil,  and  absolutely  no  current  would  flow  in  the  main  circuit. 
The  filter  effect  would  be  perfect.  No  energy  would  therefore  flow 
from  the  source  E,  but  this  would  merely  give  the  condenser  an 
initial  charge,  and  thereafter  current  would  flow  between  the  two 
branch  circuits,  even  if  the  main  circuit  were  removed.  See  Section 
115,  on  free  oscillations. 

In  any  actual  case  there  must,  however,  be  some  resistance  in  the 
circuit,  and  the  energy  for  the  heating  in  the  resistance  must  come 
from  outside.  The  emf.  E  must  cause  just  enough  current  to  flow 
in  the  main  circuit  to  make  good  this  loss  of  energy.  It  is  easy  to 
show  that  these  conclusions  follow  also  from  the  equations  previ- 
ously cited.  When  the  resonance  condition  is  established,  the  main 
current  and  the  emf.  E  are  in  phase,  so  that  the  power  is  equal  to 

77»2  D 

the  product  of  the  emf.  E  and  the  main  current,  that  is, 


The  power  lost  in  heating  is  equal  to  the  square  of  the  current  in 
the  coil  multiplied  by  the  resistance  of  the  coil.     The  current  in  the 

Tfl 

coil  is,  however  (Section  57),  /p2-~/9    fr&  so  that  the  power  in  heat- 

TjY2  T> 

ing  has  the  value  y^i/?  —  jr^2  as  before.     The  fact  that  the  main 


current  should  be  zero,  when  the  resistance  is  zero,  is  in  line  with 
equation  (76)  for  7,  and  with  the  fact  also  that  the  heating  must  be 
zero  in  that  case. 


RADIO    COMMUNICATION.  199 

Besides  tuning  the  filter  by  varying  the  capacitance,  it  is  of  course 
possible  to  obtain  parallel  resonance  by  varying  the  inductance 
instead.  For  a  given  coil  and  condenser,  it  is  also  possible  to  obtain 
parallel  resonance  by  adjusting  the  frequency  of  the  applied  emf. 
It  must  be  noted,  however,  that  when  either  the  inductance  or  the 
frequency  is  varied,  the  conditions  for  minimum  current  in  the  main 
circuit  are  slightly  different  and  are  not  the  same  as  when  the 
capacitance  is  varied.  These  three  conditions  differ  appreciably 
only  when  the  resistance  is  large.  For  radio  circuits,  the  resistance 
is  usually  so  small  that  no  difference  can  experimentally  be  detected 
between  all  these  conditions  for  minimum  current.  For  zero 
resistance,  all  three  coincide  and  are  expressed  by  equation  (75). 

114.  Capacitance  of  Inductance  Coils.  —  A  coil  used  in  radio  cir- 
cuits can  seldom  be  regarded  as  a  pure  inductance.  While  the 
capacitances  between  turns  of  a  coil  are  small,  they  approach  the 
same  magnitude  as  other  capacitances  used  in  radio  circuits.  A  coil 
is  to  be  considered  as  a  combination  of  inductance  and  capacitance 
in  parallel.  It  is  found  that  the  capacitance  C0  of  a  coil  does  not 
change  appreciably  with  frequency.  Neither  does  the  inductance 
itself,  but  the  apparent  or  equivalent  inductance  La  of  this  com- 
bination of  inductance  and  capacitance  does  vary  with  frequency 
as  indicated  by  the  equation 


The  variation  with  wave  length  is  shown  in  Fig.  145.  When  the 
coil  is  the  main  coil  of  a  circuit,  it  is  usually  desirable  to  introduce 
the  emf.  into  the  circuit  by  induction  in  the  coil  itself  rather  than 
in  series  with  the  coil.  The  capacitance  of  the  coil  is  then  merely 
added  to  the  capacitance  of  the  condenser.  When  the  emf.  is  in 
series  with  the  coil,  one  effect  cf  the  coil  capacitance  is  to  increase 
the  resistance  introduced  into  the  circuit  by  the  coil  and  thus 
reduce  the  current. 

The  capacitance  of  coils  frequently  give  rise  to  peculiar  and 
undesirable  effects  in  radio  circuits.  Among  these  are  effects 
caused  by  the  capacitances  of  those  parts  of  a  coil  which  are  not 
connected  in  the  circuit.  The  turns  which  are  supposedly  "dead" 
may  actually  produce  considerable  effect,  both  upon  the  resistance 
and  frequency  of  resonance  of  the  circuit.  Thus,  the  capacitance 


200 


RADIO    COMMUNICATION. 


of  the  unused  part  2  of  the  coil  in  Fig.  146  causes  a  second  circuit 
to  be  closely  coupled  to  circuit  1.  This  may  cause  the  circuit  1  to 
respond  to  two  frequencies  and  exhibit  the  other  phenomena  of 
coupled  circuits  described  in  Section  120  below.  (See  also  C.  74, 
Sec.  19.) 

B.  Damping. 

115.  Free  Oscillations. — Thus  far  it  has  been  assumed  that  a  con- 
stant alternating  voltage  has  been  applied  to  radio  circuits,  in  which 
case  the  alternating  currents  produced  are  of  constant  amplitude. 
Such  currents  may  be  regarded  as  analogous  to  the  forced  oscillations 
which  are  produced  in  a  mechanical  system  like  a  swing  or  a  pendu- 
lum, when  it  is  acted  upon  by  a  force  which  varies  periodically. 


CHI  Fl^^,,                                        Fiq.!41 

^r^ 
i 

*    |L 

rrnirrm 

nrmm 

^ 

? 

Effect  of  dt'sTributed  eAfc>AGity 

in  the  unuseef  Turns   of  A  coil 

The  system  is  forced  to  vibrate  with  the  same  frequency  as  that 
of  the  force. 

It  is,  however,  possible  to  produce  oscillations  of  current  in  a 
circuit  without  the  necessity  of  providing  a  source  of  alternating  emf. 
A  common  method  is  merely  to  charge  a  condenser  and  then  to 
allow  it  to  discharge  through  a  simple  radio  circuit. 

This  may  be  accomplished,  for  example,  by  the  simple  means 
shown  in  Fig.  147.  By  throwing  the  switch  S  to  the  left,  the 
condenser  C  is  charged  by  the  battery  -E1,  but  when  the  switch  is 
thrown  to  the  right,  it  is  discharged  into  the  circuit  containing  the 
resistance  R  and  the  inductance  L.  If  the  resistance  R  is  not  too 
great,  electric  oscillations  are  set  up  which,  however,  steadily  die 
away  as  their  energy  is  dissipated  in  heat  in  the  resistance.  As  in 
Fig.  148,  the  current  becomes  less  and  less  as  the  oscillations  go  on. 

To  explain  this  action, we  must  follow  more  closely  what  takes  place 
in  the  circuit  from  the  moment  when  the  condenser .  charged  up  to  a 


RADIO    COMMUNICATION. 


201 


certain  potential  difference,  is  inserted  in  the  discharge  circuit. 
When  the  condenser  starts  to  discharge  itself,  a  current  flows  out  of  it, 
and  the  potential  difference  of  the  plates  decreases  as  a  result.  At 
the  moment  when  the  plates  have  reached  the  same  potential,  current 
is  still  flowing  out  of  the  condenser.  The  current  has  energy  and 
cannot  be  stopped  instantly.  In  fact,  to  bring  the  current  to  zero 
value,  it  is  necessary  to  oppose  it  by  an  emf.,  and  the  amount  of  emf. 


7TA"Trn-rE 


PIG.  I4& 

Free  oscillaTions  wiTb 
diffei~c.nT  values  of  the. 
decrement 


.  Decrement- 1 


necessary  is  greater  the  more  quickly  one  wishes  to  stop  the  current. 
It  is  similar  to  the  case  of  a  moving  body.  On  account  of  its  motion 
the  body  possesses  energy,  and  cannot  be  brought  to  rest  instantly. 
The  greater  the  force  which  is  opposed  to  it,  the  more  quickly  it  may 
be  brought  to  rest;  but  unless  its  motion  is  opposed  by  some  force,  it 
continues  to  move  indefinitely  without  change  of  velocity. 


202  RADIO    COMMUNICATION. 

The  flow  of  current  from  the  condenser,  then,  does  not  cease  when 
the  condenser  has  discharged  itself,  and,  as  a  result,  that  plate  which 
was  originally  at  the  lower  potential  takes  on  a  higher  potential  than 
the  other.  The  condenser  is  beginning  to  charge  up  in  the  opposite 
direction.  The  potential  difference  of  the  plates  now  acts  in  such  a 
direction  as  to  oppose  the  flow  of  the  current,  which  decreases  con- 
tinually as  the  potential  difference  of  the  plates  rises.  If  the  resist- 
ance of  the  circuit  were  zero,  the  current  would  be  zero  (reversing) 
at  that  moment  when  the  potential  difference  of  the  plates  had  become 
just  equal  to  the  original  value.  That  is,  the  condenser  would  be  as 
fully  charged  as  at  the  beginning,  only  with  the  potential  difference 
of  the  plates  in  the  direction  opposite  to  that  at  the  start.  Now  begins 
a  discharge  of  electricity  from  the  condenser  in  the  opposite  direction 
to  the  first  discharge,  and  this  discharging  current  flows  until  the 
condenser  has  become  fully  recharged  in  the  original  direction.  The 
cycle  of  operations  then  repeats  itself,  and  so  on,  over  and  over 
again. 

The  action  in  the  circuit  may  thus  be  described  as  a  flow  of  elec- 
tricity around  the  circuit,  first  in  one  direction  and  then  in  the  other. 
The  rate  of  flow  (current)  is  greatest  when  the  plates  have  no  poten- 
tial difference,  and  the  current  becomes  zero  and  then  begins  to  build 
up  in  the  opposite  direction  at  the  moment  when  the  potential  differ- 
ence of  the  plates  reaches  its  maximum  value.  This  alternate  flow 
of  electricity  around  the  circuit  first  in  one  direction  and  then  in  the 
other  is  known  as  an  " electrical  oscillation."  Since  no  outside 
source  of  emf.,  such  as  an  a.c.  generator,  is  acting  in  the  circuit,  the 
oscillations  are  said  to  be  "free"  oscillations. 

Mechanical  free  oscillations  are  well  known.  Such,  for  example, 
are  the  swinging  of  a  pendulum,  and  the  vibration  of  a  spring  which 
has  been  bent  to  one  side  and  then  let  go.  In  the  case  of  the  pendu- 
lum, the  velocity  with  which  it  moves  corresponds  to  the  value  of  the 
current  in  the  electrical  case,  while  the  height  of  the  pendulum  bob 
corresponds  to  the  potential  difference  of  the  condenser  plates. 
When  the  bob  is  at  its  highest  point,  its  velocity  is  zero,  corresponding 
to  the  condenser  when  the  plates  are  at  their  maximum  potential 
difference  and  no  current  is  flowing.  When  the  pendulum  bob  is  at 
its  lowest  position,  it  is  moving  most  rapidly.  Similarly,  when  the 
plates  of  the  condenser  have  zero  potential  difference,  the  current 
flowing  has  its  maximum  value.  The  pendulum  does  not  stop  mov- 
ing when  it  passes  through  its  lowest  point;  neither  does  the  current 
cease  at  the  moment  when  the  condenser  plates  are  at  the  same  po- 


RADIO    COMMUNICATION.  203 

tential.  The  pendulum  rises  with  a  gradually  decreasing  velocity 
toward  a  point  at  the  other  end  of  the  swing  as  high  as  the  starting 
point.  The  current  gradually  decreases  as  the  condenser  charges  up 
to  an  opposite  potential  difference  equal  to  the  original  value.  The 
return  swing  of  the  pendulum  corresponds  to  the  flow  of  current  in 
the  direction  opposite  to  the  original  discharge. 

A  pendulum  swinging  in  a  vacuum  and  free  from  all  friction 
would  continue  to  swing  indefinitely,  each  swing  carrying  it  to  the 
same  height  as  the  starting  point.  Similarly,  electric  oscillations 
would  persist  indefinitely  in  a  circuit,  that  is,  they  would  be  "un- 
damped "  if  there  were  no  resistance  to  the  current. 

Actually,  electric  oscillations  die  down  in  a  circuit  and  finally 
cease  altogether,  just  as  an  actual  pendulum  will  make  shorter  and 
shorter  swings  and  finally  come  to  rest.  Since  the  occurrence  of 
free  oscillations  in  a  circuit  presupposes  no  interference  with  the 
circuit  from  outside,  the  circuit  receives  no  energy  beyond  that 
imparted  to  it  at  the  moment  when  the  oscillations  begin.  There- 
after the  circuit  is  self-contained,  and  any  loss  of  its  energy  in  heat 
and  electromagnetic  waves  reduces  by  just  so  much  the  energy 
available  for  maintaining  the  oscillations.  This  loss  of  energy  goes 
on  continuously  and  the  oscillations  die  away  to  nothing.  They 
are  said  to  be  "damped"  oscillations. 

At  the  start  there  is  a  definite  amount  of  energy  present  in  the 
circuit,  namely,  the  energy  of  the  charge  given  the  condenser. 
The  amount  of  this  energy  depends  upon  the  capacitance  of  the 
condenser  and  the  square  of  the  potential  difference  between  its 
plates  (emf.  to  which  it  is  charged).  This  energy  exists  in  the 
dielectric  of  the  condenser,  which  is  in  a  strained  condition  due  to 
the  charge.  As  soon  as  the  current  begins  to  flow  the  condenser 
gives  up  some  of  its  energy,  and  this  begins  to  be  associated  with 
the  current  and  is  to  be  found  in  the  magnetic  field  around  the  cur- 
rent, that  is,  principally  in  the  region  around  the  inductance  coil. 
As  the  current  rises  in  value  under  the  action  of  the  emf.  of  the  con- 
denser, energy  is  continually  leaving  the  condenser  and  being  stored 
in  the  magnetic  field  of  the  inductance  coil.  When  the  plates  of 
.the  condenser  have  no  potential  difference,  the  whole  energy  of  the 
circuits  resides  in  the  magnetic  field  of  the  coil  and  none  in  the 
condenser.  Energy  is  then  drawn  from  the  coil  as  the  current  de- 
creases and  energy  is  stored  up  in  the  condenser  as  it  is  recharged. 

If  the  resistance  of  the  circuit  were  zero  and  no  energy  were 
radiated  in  waves  or  dissipated  in  other  ways,  the  total  energy  of 


204  RADIO    COMMUNICATION. 

the  circuit  would  be  constant.  The  energy  dissipated  in  heat  and 
electric  waves  is,  however,  lost  to  the  circuit,  so  that  the  total  amount 
of  energy,  found  by  adding  that  present  in  the  condenser  to  that  in 
the  inductance,  steadily  decreases.  Finally  all  the  original  store  of 
energy  given  the  circuit  has  been  dissipated  and  the  oscillations 
cease. 

The  energy  lost  when  a  steady  current  is  flowing  in  a  circuit  de- 
pends not  only  on  the  value  of  the  current,  but  on  the  resistance 
of  the  circuit,  and  in  a  radio  circuit  this  resistance  is  replaced  by  a 
somewhat  larger  quantity  of  the  same  kind,  the  "effective  resist- 
ance." (See  Sec.  117.)  The  greater  the  effective  resistance,  the 
greater  the  amount  of  energy  dissipated  per  second  when  a  given 
current  flows. 

Ohm's  law  shows  that  to  keep  a  current  I  flowing  through  a  resist- 
ance R  an  emf.  Rlis  necessary  and  this  has  to  be  furnished  by  the 


FlO     I5o 


.04.-,--. 


v .' .  Hi-'.':,iT->---^j^ 


Emf  induced  in  the  cross  section    of  a 
Conductor  CArrylrfe  hi^h  frequency  current 


battery,  generator,  or  other  source.  In  an  oscillating  circuit  the 
same  is  true,  and  that  portion  of  the  emf.  in  the  circuit  which  is 
employed  in  forcing  the  current  against  the  resistance  is  of  course 
not  available  for  charging  the  condenser  or  building  up  the  dis- 
charge current.  The  changes  of  current  in  the  circuit  described  above 
are  thereby  hindered,  and  the  current  does  not  rise  to  as  great  a  value 
as  it  would  in  the  absence  of  resistance.  The  maximum  of  emf. 
between  the  plates  of  the  condenser  is  less  each  time  the  condenser 
is  discharged,  and  thus  the  oscillations  of  the  current  die  away. 

A  good  analogy  to  damped  electrical  oscillations  in  a  circuit  is 
found  in  the  vibrations  of  a  flat  spring,  clamped  at  one  end  in  a  vise, 
and  then  bent  to  one  side  and  released,  Fig.  149.  The  spring 
vibrates  from  side  to  side  with  decreasing  amplitude,  until  finally 
it  comes  to  rest  in  its  unbent  position  0.  When  the  spring  is  bent, 
energy  is  stored  up  in  it — the  energy  of  bending.  On  being  released 


RADIO    COMMUNICATION.  205 

the  spring  moves  and  gains  energy  of  motion,  while  the  energy  of 
bending  decreases.  If  there  were  no  friction,  the  loss  of  one  kind 
of  energy  would  be  just  offset  by  the  gain  of  the  other  kind  and  the 
sum  total  would  remain  constant.  The  spring  would  move  past  the 
natural  undisturbed  position  0,  under  the  influence  of  its  energy  of 
motion,  and  would  be  brought  to  rest  at  a  position  just  as  far  to  the 
other  side  of  0  as  was  the  starting  point. 

Friction  has,  however,  the  effect  of  opposing  the  motion  and  caus- 
ing a  dissipation  of  energy  in  heat,  and  each  excursion  away  from 
the  resting  point  is  smaller  than  the  one  preceding. 

Free  oscillations,  then,  can  take  place  in  a  circuit  containing  in- 
ductance and  capacitance.  These  would  be  undamped  in  the  ideal 
case  where  the  resistance  can  be  regarded  as  zero.  In  all  practical 
cases  of  free  oscillations,  however,  the  oscillations  are  damped.  To 
produce  undamped  waves  it  is  necessary  to  provide  some  source  of 
power  to  make  good  the  energy  dissipated  in  the  oscillating  circuit. 
Strictly  speaking,  undamped  free  oscillations  are  impossible  in 
actual  circuits.  It  is  of  importance  to  study  the  effect  of  the  resist- 
ance in  determining  the  rapidity  with  which  the  oscillations  die 
away. 

116.  Frequency,  Damping,  and  Decrement  of  Free  Oscillations. — • 
If  the  resistance  of  the  oscillating  circuit  is  constant,  it  is  possible  to 
calculate  the  period  of  the  free  oscillations  in  the  circuit  and  to  find 
the  rate  at  which  the  oscillations  die  away.  If  L,  C  and  R  are. 
respectively,  the  inductance,  capacitance,  and  resistance  of  the  cir- 
cuit, then  free  oscillations  in  the  circuit  will  have  the  frequency 

(78) 

This  is  known  as  the  "natural  frequency"  of  the  circuit.  Similar 
considerations  apply  to  the  pendulum  and  vibrating  spring  discussed 
above.  Each  vibrates  in  a  period  natural  to  it,  which  depends  upon 
the  dimensions,  material  of  the  vibrating  system,  and  the  friction 
against  which  it  moves. 

R2 
If  it  snould  happen,  in  any  case,  that  the  quantity  ^-2  is  equal 

to  or  greater  than  -j^  tnen  free  oscillations  in  the  circuit  are  impos- 
sible; the  current  in  the  circuit  does  not  reverse  its  direction  at  all, 
but  simply  dies  away.  The  circuit  is  said  to  be  in  the  "aperiodic'* 


206  RADIO    COMMUNICATION. 

condition,  that  is,  without  period.  Seldom  do  such  cases  occur  in 
radio  circuits.  Usually,  the  quantity  4^2  instead  of  being  larger 
than  •££»  is  very  small  in  comparison  with  the  latter.  We  may  there- 
fore as  a  rule,  use  without  error  as  the  expression  for  the  natural  period 

(79> 


which  is  the  same  expression  as  for  the  frequency  of  the  applied  emf  . 
necessary  in  order  that  the  circuit  shall  be  in  the  resonance  condi- 
tion. 

The  rapidity  with  which  the  oscillations  die  away  depends,  not 
only  on  the  resistance  of  the  circuit,  but  on  the  inductance  also. 
The  greater  the  resistance  and  the  smaller  the  inductance,  the  more 
rapid  is  the  damping  and  the  rate  at  which  the  oscillations  decrease. 
If  the  resistance,  capacitance,  and  inductance  of  the  circuit  have 
fixed  values,  it  may  be  shown  that  each  successive  maximum  of 
current  is  the  same  fraction  of  the  preceding  maximum,  as  the  latter 
is  of  the  maximum  immediately  preceding  it.  If,  for  example,  the 
second  maximum  is  0.9  of  the  first,  the  third  will  be  0.9  of  the  second, 
etc.  However,  instead  of  adopting  as  a  numerical  measure  of  the 
rate  of  decrease,  this  ratio  itself,  it  is  found  more  convenient  in  the 
mathematical  theory  of  damping  to  adopt  the  natural  logarithm  of 
the  ratio  of  any  maximum  to  the  next  following  maximum  with  the 
current  in  the  same  direction,  i.  e.,  the  logarithm  of  the  ratio  of  two 
maxima  one  cycle  apart.  This  number  is  known  as  the  '  '  logarithmic 
decrement,"  or  "decrement,"  for  short. 

In  cases  where  the  resistance  of  the  circuit  is  not  exceedingly  large, 
the  decrement  is  equal  to  TT  times  the  quotient  of  the  resistance  by 
the  inductive  reactance  of  the  circuit,  calculated  for  the  natural 


frequency  of  the  circuit.    That  is,  the  decrement  is  equal  to  w 

so  that  increasing  the  resistance  or  decreasing  the  inductance,  both 
increase  the  decrement.  The  natural  frequency  being  practically 
independent  of  the  resistance,  that  is,  equation  (79)  being  suffi- 
ciently accurate,  the  capacitive  reactance  is  equal  to  the  inductive 
reactance.  Thus  the  decrement  is  ?r  times  the  quotient  of  the  resist- 
ance by  the  capacitive  reactance  at  the  natural  frequency  of  the 
circuit. 


RADIO    COMMUNICATION.  207 

Examples  of  Decrements, — Fig.  148  gives  a  graphic  idea  of  the 
dissipation  of  the  oscillations  in  three  cases  where  the  decrements  are 
0.01,  0.1,  and  1.  These  correspond  to  circuits  of  very  small  damping, 
moderate  damping,  and  excessive  damping,  respectively.  Each 
curve  starts  from  the  same  .value  of  current  at  the  first  maximum, 
and  for  each  the  natural  period  of  the  circuit  is  the  same.  The 
latter  is  represented  by  the  horizontal  distance,  AB,  B C,  etc.,  in 
each.  The  difference  between  the  curves  is  striking.  In  the  case  of  a 
decrement  of  0.01,  the  oscillations  decrease  only  very  gradually;  this 
case  approximates  that  of  undamped  waves.  In  the  extreme  case  of 
a  decrement  of  1,  the  oscillations  become  negligible  after  only  four 
or  five  periods.  To  construct  such  curves  the  following  simple 
method  may  be  used. 

Assume  a  certain  number  of  divisions  in  the  horizontal  direction  to 
represent  the  period  of  the  oscillations,  for  example,  five.  Then  the 
curve  must  cross  the  horizontal  axis  every  two  and  one-half  divisions. 
Choose  a  convenient  number  of  divisions  to  represent  the  first  maxi- 
mum of  the  current,  for  example,  ten.  The  curves  DE  (Fig.  148)  are 
next  drawn  to  scale,  starting  with  the  chosen  value  for  the  first  maxi- 
mum. The  curves  DE  have  the  property  that  the  height  of  the  curve 
falls  off  by  equal  fractions  of  its  value  for  equal  horizontal  intervals. 

For  instance,  if  the  decrement  is  0.1,  we  find,  since  0.1  is  the  nat- 
ural logarithm  of  1.105,  that  the  first  maximum  OD  in  the  positive 
direction  is  1.105  times  as  great  as  the  next,  PG,  and  so  on  for  any 
two  successive  maxima  in  the  same  direction.  If,  therefore,  we 

take  OD= 10  division,  PG  will  equal  ;Qn5=9-05  division,  RH  will  be 

9  05 

-.  '    -=8.19,  etc.    The  oscillations  must  be  confined  between  the 

two  curves  DE,  and  since  the  crossing  points  have  also  been  located,  as 
as  well  as  the  positions  of  the  maxima,  it  is  not  difficult  to  sketch  in 
the  curve  of  oscillations  free  hand,  making  the  loops  of  approximately 
sine  shape. 

Number  of  Oscillations. — Although,  strictly  speaking,  the  oscilla- 
tions never  would  become  absolutely  zero,  they  actually  become 
negligible  after  a  certain  time.  A  knowledge  of  the  logarithmic  de- 
crement enables  us  to  calculate  how  many  complete  oscillations  will 
be  executed  before  their  amplitude  has  fallen  below  a  certain  frac- 
tion of  the  first  oscillation.  This  number  is  greater  the  smaller  the 
decrement. 


208  RADIO   COMMUNICATION. 

If,  for  example,  we  arbitrarily  choose  to  find  the  number  of 
oscillations  which  will  be  completed  before  the  maximum  of  current 
will  fall  below  1  per  cent  of  the  value  at  the  start,  we  have  simply 
to  take  the  quotient  of  the  natural  logarithm  of  100  by  the  decrement. 
The  natural  logarithm  of  100  is,  near  enough,  4.6.  The  number  of 
oscillations  is  thus  4.6  divided  by  the  decrement.  Thus  in  the  three 
cases  given  in  Fig.  148  the  numbers  of  complete  oscillations  will 
be  460,  46  and  4.6,  corresponding  to  the  decrements  0.01,  0.1,  and 
1,  respectively. 

The  maximum  possible  value  of  decrement  would  be  infinite, 
but  the  United  States  radio  laws  require  that  values  greater  than 
0.2  shall  not  be  used  on  account  of  the  interference  of  highly  damped 
stations  with  other  stations.  The  number  of  complete  oscillations 
calculated  by  the  above  rule  is  23  for  a  decrement  of  0.2. 

The  decrement  gives  an  idea  of  the  efficiency  of  a  sending  appa- 
ratus. The  smaller  the  decrement,  the  sharper  the  tuning  possible, 
and,  therefore!  the  greater  the  proportion  of  the  emitted  energy 
which  can  be  utilized  in  the  receiving  apparatus.  The  larger  the 
decrement  the  larger  the  proportion  of  energy  which  serves  no 
useful  purpose,  and  which  may  cause  serious  d  isturbance  to  other 
stations. 

In  the  case  of  a  spark  circuit  the  idea  of  logarithmic  decrement 
is  not  exactly  applicable.  On  account  of  the  variable  resistance 
of  the  spark,  the  oscillations  fall  off  according  to  a  different  law 
than  that  just  discussed.  (See  C.  74,  p.  230.) 

C.  Resistance. 

117.  Resistance  Ratio  of  Conductors. — When  a  steady  emf.  is 
applied  between  the  ends  of  a  conductor,  the  current  quickly  rises 
to  the  final  Ohm's  law  value,  and  distributes  itself  uniformly  over 
the  cross  section  of  the  wire.  During  the  interval  between  the  mo- 
ment when  the  emf.  is  applied,  and  the  moment  of  attainment  of  the 
final  steady  state,  the  current  distribution  over  the  cross  section  is 
not  uniform.  This  effect  is  due  to  self-induced  emfs.  in  the  cross 
section  of  the  conductor.  Suppose  that  a  section  be  taken  through 
the  axis  of  a  cylindrical  conductor  and  that  the  applied  emf.  tends 
to  produce  a  current  in  the  direction  of  the  arrow  (Fig.  150).  The 
magnetic  lines  in  the  cross  section  will  be  circles,  in  planes  at  right 
angles  to  the  axis,  and  with  their  centers  in  the  axis.  In  the  figure, 
the  lines  will  be  directed  out  of  the  paper  in  the  region  above  the  axis 


RADIO   COMMUNICATION.  209 

and  into  the  paper  in  the  region  below  the  axis.  As  the  total  cur- 
rent rises  in  value,  the  number  of  lines  of  force  through  any  portions 
of  the  cross  section,  such  as  ABCD  and  EFGH,  will  be  increasing, 
and  by  Lenz's  law  (Sec.  45)  this  change  of  field  will  give  rise  to 
induced  emfs.  which  tend  to  oppose  the  changes  of  the  field.  The 
directions  of  these  induced  emfs.  will  accordingly  be  those  indicated 
by  the  small  arrows,  and  it  is  easy  to  see  that  the  increase  of  the 
current  is  aided  in  those  portions  of  the  cross  section  which  lie  near 
the  surface  of  the  conductor,  and  hindered  at  the  portions  nearer  the 
axis.  That  is,  the  current  reaches  its  final  value  later  at  the  axis 
of  the  cross  section  than  at  points  on  the  surface  of  the  wire.  On 
the  other  hand,  if  the  circuit  is  broken  after  the  distribution  ot 
current  has  reached  the  uniform  state,  the  outer  portions -of  the 
conductor  will  first  be  free  from  current. 

These  effects  may  be  accurately  described  by  the  statement  that 
the  current  grows  from  the  outer  layers  of  the  wire  inward,  and  that 
the  current  inside  the  conductor  attains  the  same  value  as  that  at 
the  surface,  only  after  a  finite  interval  of  time. 

When  a  rapidly  alternating  emf .  is  impressed  upon  the  conductor, 
(a)  the  phase  of  the  current  inside  the  conductor  lags  behind  that  of 
the  current  at  the  surface  by  an  amount  which  is  greater  the  nearer 
the  point  is  to  the  axis;  and  (6)  the  amplitude  of  the  current  is  largest 
at  the  surface  and  decreases  as  the  axis  is  approached  because 
sufficient  time  has  not  been  allowed  for  the  final  steady  value  to  be 
reached  before  the  emf.  was  changed .  This  non-uniformity  of  current 
distribution  in  the  cross  section  is  known  as  the  ''skin  effect,"  and 
it  is  equivalent  to  a  reduction  of  the  cross  section  of  the  conductor 
with  consequent  increase  in  its  resistance. 

From  these  considerations,  it  will  be  seen  that  in  addition  to  its 
dependence  on  the  frequency,  the  skin  effect  will  be  more  serious, 
the  thicker  the  conductor  and  the  greater  the  permeability  and 
conductivity  of  the  material  of  which  it  is  composed;  for  the  thicker 
the  conductor,  the  longer  the  interval  which  must  elapse  before  a 
change  in  emf.  will  be  felt  at  the  center  of  the  conductor  and  thus 
the  greater  the  difference  in  the  current  density  at  different  points 
of  the  cross  section.  With  given  dimensions,  the  greater  the  per- 
meability of  the  wire,  the  greater  the  emf.  induced  in  its  mass.  The 
better  the  conductivity,  the  less  the  ratio  of  the  effectivo  current 
to  the  value  at  the  surface. 
97340°— 19 14 


210  RADIO    COMMUNICATION. 

A  numerical  calculation  of  the  magnitude  of  the  skin  effect  can 
be  made  only  in  a  few  special  cases  for  which  Circular  74,  pages 
299-308,  should  be  consulted.  Table  18  of  Circular  74  will  enable 
one  to  see  at  a  glance  how  great  diameter  of  wire  is  allowable,  in 
order  that  the  increase  of  resistance  due  to  skin  effect  shall  not 
exceed  1  per  cent  of  the  direct  current  value.  Such  data  are  of 
use  in  estimating  the  size  of  wire  suitable  for  a  hot  wire  ammeter, 
in  order  that  its  resistance  may  not  vary  in  the  range  of  frequency 
for  which  it  is  intended.  For  larger  diameters  of  wire  the  effect 
increases  rapidly  and  cases  where  the  high  frequency  resistance  is 
five  to  ten  times  the  direct  current  value  are  not  rare.  These 
facts  must  be  kept  in  mind  when  estimating  the  current  carrying 
capacity  of  a  conductor.  The  "resistance  ratio"  is  defined  as  the 
ratio  of  resistance  at  the  frequency  in  question  to  the  resistance  to 
direct  current.  Then,  for  the  same  heating,  the  allowable  current 
at  the  high  frequency  will  be  less  in  the  ratio  of  the  square  root 
of  the  resistance  ratio. 

Since  the  skin  effect  tends  to  render  useless  for  the  carrying  of 
the  current  the  inner  portions  of  the  cross  section  of  a  wire,  thin  tub- 
ing, or  a  thin  layer  of  good  conducting  m?terial  plated  on  the  surface 
of  a  poor  conducting  cylinder  is  a  form  of  conductor  suitable  for 
carrying  currents  of  radio  frequency.  In  fact,  tubing  which  is  very 
thin  in  comparison  with  its  radius  has  for  the  same  cross  section  a 
smaller  high  frequency  resistance  than  any  other  single  conductor. 

To  reduce  the  skin  effect,  a  conductor  is  often  built  up  of  a  number 
of  very  fine  conducting  strands.  The  resistance  ratio  of  such  a 
combination  is,  however,  on  account  of  the  mutual  inductance  of 
the  strands,  appreciably  greater  than  the  resistance  ratio  of  one  of 
the  strands.  To  be  effective,  the  strands  should  be  placed  as  far 
apart  as  practicable,  and  the  diameter  of  the  individual  strands 
should  not  exceed  about  0.1  mm.  The  most  effective  form  of 
stranded  conductor,  although  expensive  to  make,  is  one  where 
the  strands  are  so  twisted  as  to  form  a  woven  tube.  For  further 
particulars  see  pages  306-308,  of  Circular  74. 

Effective  Resistance. — The  resistance  of  a  circuit  at  high  frequency 
is  never  the  same  as  the  resistance  measured  by  direct  current. 
To  define  what  is  meant  by  the  resistance  at  high  frequencies,  we 
have  to  divide  the  power  lost  in  heating  or  otherwise  dissipated,  by 
the  square  of  the  effective  current.  This  quotient  is  known  as  the 
"  effective  resistance"  at  the  frequency  in  question. 


RADIO    COMMUNICATION.  211 

The  effective  resistance  of  a  circuit  carrying  currents  of  radio 
frequency  may  be  very  appreciably  affected  by  the  presence  of 
neighboring  conducting  bodies.  The  energy  of  any  eddy  currents 
which  may  be  induced  in  the  latter  is  drawn  from  the  circuit  in  ques- 
tion, whose  effective  resistance  is  thereby  increased.  On  account 
of  the  high  frequency,  this  effect  can  be  astonishingly  large  in  good 
conductors  and  may  be  appreciable  in  the  presence  of  such  a  poor 
conducting  path  as  a  painted  surface. 

Different  portions  of  the  same  circuit  should  not  be  placed  in 
close  proximity.  The  mutual  effects  of  the  currents  which  flow  in 
opposite  directions  in  two  parallel  cylindrical  wires  is,  for  example, 
such  as  to  cause  the  maximum  current  densities  in  the  two  cross 
sections  to  be  shifted  to  points  nearer  the  other  conductor,  with  an 
increase  in  the  effective  resistance  of  each  conductor  above  the  value 
it  would  possess  in  the  absence  of  the  other.  In  other  cases  (p.  302, 
C.  74)  the  effective  resistance  may  be  reduced  by  the  presence  of 
the  other  lead.  An  important  example  of  the  effect  of  the  mutual 
inductance  of  neighboring  conductors  on  their  effective  resistances 
is  furnished  by  a  system  of  parallel  wires  connected  in  parallel.  In 
this  case  more  current,  at  radio  frequencies,  flows  in  the  outer  wires 
than  in  the  inner,  and  the  differences  may  become  very  important. 
This  is  a  point  which  cannot  be  overlooked  in  the  design  of  hot  wire 
ammeters  to  carry  large  currents. 

118.  Brusji,  Spark,  Dielectric,  and  Radiation  Resistance. — As 
has  already  been  explained  (Sees.  31  and  58),  no  dielectric  is  perfect. 
Some  heating  takes  place  in  it,  and  we  may  artificially  represent  a 
condenser  as  equivalent  to  a  pure  capacitance  in  series  with  a 
resistance.  The  introduction  of  a  condenser  into  a  radio  circuit  has 
therefore  the  effect  of  increasing  the  effective  resistance  of  the 
circuit,  and,  except  in  especially  designed  air  condensers,  this  effect 
cannot  be  neglected.  Care  needs  therefore  to  be  taken  that  poor 
dielectric  materials  be  kept  away  from  regions  of  intense  electric 
field. 

When  operating  condensers  at  high  voltages,  large  energy  losses 
may  occur  in  the  so-called  brush  discharge,  and  this  effect  will 
generally  give  rise  to  a  very  considerable  increase  in  the  effective 
resistance  of  the  condenser. 

If  a  spark  gap  is  included  in  a  circuit,  the  resistance  of  the  spark 
will  have  to  be  included  in  the  total  effective  resistance  of  the 
circuit.  This  spark  resistance  depends  upon  a  number  of  circum- 
stances, and  the  laws  of  its  variation  are  very  complex.  In  general, 


212 


RADIO    COMMUNICATION. 


a  short  spark  gap  has  a  larger  conductivity  per  unit  length  than  a 
long  one.  Thus  a  series  of  short  spark  gaps  is  better  than  a  single 
one  of  the  same  length  as  the  sum  of  the  lengths  of  the  shorter  gaps. 
The  pressure  and  nature  of  the  gas  between  the  terminals  also  affect 
the  resistance  which  is  materially  decreased  with  reduction  of 
pressure.  Further,  the  nature  of  the  terminals  and  the  constants  of 
the  remainder  of  the  circuit  all  affect  the  spark  resistance. 

Some  of  the  power  supplied  to  a  circuit  which  is  carrying  a  radio 
current,  is  radiated  from  the  circuit  in  the  form  of  electromagnetic 
waves  (see  Chap.  5).  This  may  be  regarded  as  the  useful  work 
obtained  from  the  circuit,  and  for  transmission  purposes  the  power 
radiated  should  be  made  as  large  as  possible,  in  comparison  to  the 
power  dissipated  in  the  circuit  itself,  and  in  its  immediate  surround- 
ings. The  power  radiated  at  any  frequency  is  found  to  be  propor- 
tional to  the  square  of  the  current  flowing,  so  that  the  radiative 


Ty  fees     of  cou^linV  )    fa)  di'rect cou^linV       (b)    mdvot 
'' 


effect  may  be  regarded,  artificially,  as  causing  a  definite  increase  in 
the  effective  resistance  of  the  circuit.  This  fictitious  resistance 
increase  is  known  as  the  "radiation  resistance,"  and  is  found  to  be 
directly  proportional  to  the  square  of  the  frequency,  or  inversely 
proportional  to  the  square  of  the  wave  length. 

D.  Coupled  Circuits. 

119.  Kinds  of  Coupling. — When  two  circuits  have  some  part  in 
common,  or  are  linked  together  through  a  magnetic  or  an  electrostatic 
field,  they  are  said  to  be  "coupled."  When  the  part  in  common  is 
an  inductance  (Fig.  151-a),  the  two  portions  of  the  circuit  are  said 
to  be  "direct  coupled."  In  Fig.  151-c  the  part  in  common  is  a 
capacitance  and  this  gives  an  example  of  "capacitive  coupling." 
In  the  important  case  in  which  the  circuits  are  mutually  inductive 


RADIO    COMMUNICATION.  213 

(Fig.  151-b)  the  circuits  are  said  to  be  "inductively  coupled."" 
More  rarely  the  coupling  is  an  "electrostatic"  kind  in  which  the 
plates  of  a  condenser  in  one  circuit  are  placed  between  those  of  a, 
condenser  in  the  other  circuit. 

It  is  customary  to  denote  as  the  "primary"  that  circuit  in  which 
the  applied  emf.  is  found,  the  other  being  regarded  as  the  "sec- 
ondary "  circuit.  When  two  circuits  are  coupled  they  react  on  one 
another  so  that  the  current  in  each  circuit  is  not  the  same  as  would 
be  the  case  were  the  other  circuit  absent.  The  extent  of  the  re- 
action is,  however,  very  different  in  different  cases.  Circuits  are 
said  to  be  "closely  coupled"  when  any  change  in  the  current  in 
one  is  able  to  produce  considerable  effects  in  the  other.  When 
either  circuit  is  little  affected  by  the  other,  the  coupling  is  regarded 
as  "loose."  The  coupling  between  two  inductively  coupled  cir- 
cuits is  made  looser  by  increasing  the  distance  between  the  two- 
coupling  coils. 

A  more  exact  measure  of  the  closeness  of  the  coupling  is  given  by 
what  is  called  the  "coefficient  of  coupling"  (denoted  by  k).  Its 
value  in  the  case  of  direct  coupling  (Fig.  151-a)  is  given  by 

(80> 


If  the  total  inductances  of  the  circuits  in  Fig.  151-b  are  denoted 
by  Ll  and  L2,  we  have  for  inductive  coupling 


and  for  capacitive  coupling  (Fig.  151-C), 

(82) 


As  the  coupling  is  made  very  loose,  k  approaches  zero  as  its  limit 
for  the  closest  possible  coupling  k  would  be  unity. 

The  coupling  of  two  direct  coupled  circuits  may  be  increased  by 
increasing  the  amount  of  inductance  which  is  common  to  the  two- 
circuits,  maintaining  constant  the  total  inductances  (La+Jf)  and 
(Lb+  M]  of  the  two  circuits.  To  make  the  coupling  of  the  induc- 
tively coupled  circuits  closer,  their  mutual  inductance  is  increased 
by  moving  the  coils  nearer  or  by  increasing  the  inductance  of  either 
coil.  For  example,  the  coefficient  of  coupling  of  an  antenna  may 


214  RADIO    COMMUNICATION. 

be  increased  by  adding  turns  to  the  coil  of  the  oscillation  trans- 
former, enough  inductance  being  subtracted  from  the  loading  coil 
to  keep  the  total  inductance  of  the  circuit  constant.  Capacitive 
coupling  is  closer,  the  smaller  the  common  capacity  Cm  is  in  com- 
parison with  the  capacities  Ca  and  Cb. 

In  some  types  of  receiving  apparatus  the  coupling  condenser  is 
connected  in  a  different  manner  from  that  shown  in  Fig.  151-c 
(see  Sec.  177),  and  in  that  case  the  coupling  is  loosened  by  a  decrease 
of  capacitance  in  the  coupling  condenser. 

The  reaction  of  either  circuit  on  the  other  affects,  not  only  the 
value  of  the  currents  in  the  coils,  as  would  be  expected,  but  has  an 
important  influence  on  the  frequency  to  which  the  circuits  respond 
most  vigorously.  This  is  explained  in  the  following. 

120.  Double  Hump  Resonance  Curve. — It  may  be  shown  (Sees. 
16  to  18  of  C.  74)  that  the  reactance  of  either  of  the  circuits,  primary 
or  secondary,  is  zero,  that  is,  the  impedance  is  a  minimum,  for  two 
separate  frequencies/7  and/77,  which  are  different  from  the  natural 
frequencies/!  and/2,  for  which  the  primary  and  secondary  circuits 
are  in  resonance  when  taken  alone.  With  loose  coupling/7  and/77 
differ  little  from/!  and/2.  With  closer  coupling,  however,  the  dif- 
ferences become  very  appreciable.  If  f  be  used  to  denote  the 
lower  of  these  two  frequencies,  then  it  may  be  shown  that/7  is 
always  still  lower  than  the  lower  of  the  two  natural  frequencies  / 
and  /2,  while  the  higher  frequency  /7/  is  always  higher  than  the 
higher  of  the  two  natural  frequencies.  Increasing  the  closeness  of 
the  coupling  has  always  the  effect  of  spreading  /7  and  /77  further 
apart.  Furthermore,  the  difference  between  /7/  and  the  higher  of 
the  two  natural  frequencies  is  always  greater  than  the  corresponding 
difference  between/7  and  the  lower  of  the  natural  frequencies. 

These  conclusions  may  be  tested  by  means  of  a  wavemeter.  As 
has  been  already  pointed  out  (Sec.  112),  the  current  induced  in  a 
wavemeter  circuit  is  a  maximum  when  the  wavemeter  is  tuned  to 
the  frequency  of  the  exciting  current.  Suppose  the  wavemeter  to 
be  very  loosely  coupled  to  either  the  primary  circuit  or  the  sec- 
ondary. Let  the  frequency  of  the  current  in  the  primary  be  varied 
by  small  steps  and  adjust  the  setting  of  the  wavemeter  for  each  fre- 
quency until  the  indicator  shows  a  maximum  current  in  the  wave- 
meter  circuit.  If  the  settings  of  the  wavemeter  condenser  and  the 
corresponding  deflections  of  the  indicating  instrument  are  plotted, 
a  resonance  curve  is  obtained  which  will  show  two  humps  or  peaks 
corresponding  to  the  frequencies  /7  and  /7/.  The  positions  of  the 


RADIO    COMMUNICATION.  215 

two  humps  will  be  found  to  be  different  for  a  second  resonance  curve, 
taken  with  a  different  coupling  between  the  primary  and  the  sec- 
ondary. The  coupling  between  the  wavemeter  circuit  and  the 
circuit  which  is  exciting  it  must  be  made  as  loose  as  practicable  in 
order  that  the  wavemeter  circuit  may  not  react  appreciably  on  the 
other  circuits  and  thus  change  their  currents. 

A  more  direct  method  of  showing  the  two  frequencies  is  furnished 
by  simply  inserting  a  hot  wire  ammeter  or  thermocouple  in  the 
circuit  to  be  examined  and  noting  the  changes  in  its  readings  as  the 
frequency  is  continuously  varied. 

In  the  case  of  the  usual  coupled  radio  circuits,  the  two  circuits, 
primary  and  secondary,  are  adjusted  independently  to  the  same 
natural  frequency.  That  is,  /t  is  made  equal  to  /2.  When  the 
coupling  is  made  loose,  both  f  and  f"  approach  the  same  value, 
/"  from  above  and  f  from  below,  and  at  very  loose  coupling, 

'//-/f/7/i-/i. 

It  might  be  supposed  that  in  the  special  case  where  fi=/2,  the  cur- 
rents in  the  circuits  would  be  a  maximum  for  a  single  frequence  only, 
namely,  at  the  value  of/  to  which  they  are  both  tuned.  Never- 
theless, both  experiment  and  theory  show  that  each  circuit,  even 
in  this  case,  offers  a  minimum  impedance  at  two  different  fre- 
quencies, just  as  is  found  for  the  more  general  case.  The  two  fre- 
quencies f  and  /"  lie  on  either  side  of  the  value  /,  though  not  at 
equal  intervals  from  the  latter,  the  difference  /"  — /  being  always 
greater  than/— /'. 

When/!=/2,  the  effect  of  the  coupling  on  the  values  of/'  and/x/ 
is  shown  by  the  simple  relations 

/•/_  /_     /•"=  -L, 
3    Vi+t      •*     Vra 

If  the  coupling  is  made  more  and  more  loose,  the  two  frequencies 
/'  and/"  approach  one  another,  and  the  two  humps  of  the  resonance 
curves  finally  merge  and  become  indistinguishable  from  a  single 
hump. 

In  the  absence  of  a  secondary  current,  there  is  no  reaction  on  the 
primary,  which  is  no  longer  a  coupled  circuit,  and  will  necessarily 
be  in  resonance  at  a  single  frequency  only  (/by  hypothesis).  The 
same  remarks  apply  to  the  secondary  when  the  primary  circuit  is 
broken. 

The  further  treatment  of  coupled  circuits  naturally  follows  two 
different  lines,  according  to  whether  the  primary  is  excited  by  a 


216  RADIO    COMMUNICATION. 

sine  wave  of  a  definite  frequency  (producing  oscillations),  or  whether 
the  primary  circuit  is  given  a  single  impulse  and  then  allowed  to 
oscillate  freely. 

121.  Forced  Oscillations.  —  When  a  sine  emf.  of  frequency  /  is 
applied  to  the  primary,  the  currents  in  the  two  circuits,  primary  and 
secondary,  are  at  first  very  complicated,  consisting  of  oscillations 
of  the  two  frequencies  /'  and  /x/,  superposed  upon  forced  waves  of 
frequency/.  The  free  oscillations  quickly  die  away,  and  there  re- 
main sine  currents  of  frequency  /in  both  the  primary  and  secondary. 

High  Frequency  Transformer.  —  It  can  be  shown  that  to  obtain  the 
maximum  current  in  the  secondary  circuit,  a  certain  value  of  the 
coupling  of  the  coils  is  necessary.  If  the  coupling  be  made  either 
closer  or  looser  than  this  value,  the  secondary  current  falls  off  in 
value.  In  general,  the  proper  coupling  for  maximum  secondary 
current  will  depend  upon  the  resistances  of  the  primary  and  sec- 
ondary and  their  reactances,  and  can  be  determined  better  by  actual 
experiment  than  by  calculation.  For  one  important  case,  however, 
the  values  of  the  coupling  and  the  maximum  secondary  current  can 
be  expressed  very  simply. 

If  the  primary  and  secondary  circuits  are  separately  tuned  to  the 
frequency  of  the  applied  alternating  emf.  E,  the  maximum  possible 

E 

secondary  current  has  the  value  I2=—j===  where  Ri  and  R2  are  the 


primary  and  secondary  resistances.  The  value  of  the  mutual  induct- 
ance (coupling)  which  gives  the  maximum  secondary  current  may 
be  calculated  from  the  relation  2irfM=-jR1  R2.  The  primary  current 

Tf\ 

under  these   circumstances  assumes   the  value  I\=2W  which  is 

one-half  the  resonance  value  of  the  primary  current  when  the  sec- 
ondary is  absent. 

These  relations  and  the  dependence  of  the  secondary  current  on 
the  coupling  are  illustrated  in  Fig.  152,  which  shows  the  changes  of 
the  secondary  current  as  the  mutual  inductance  between  the  coils 
is  varied.  The  resistances  R1=2.0  and  R2=12.5  ohms  are  assumed, 
and  the  secondary  current  is  plotted  in  terms  of  its  maximum  value, 
which  is  taken  as  1.  As  abscissas  are  taken,  not  the  mutual  induct- 
ance itself  but  2-irfM,  so  that  the  curve  is  applicable  to  different  fre- 
quencies, assuming,  of  course,  that  in  every  case  the  two  circuits  are 
tuned  to  the  frequency  in  question.  Maximum  secondary  current 
is,  in  this  example,  obtained  for  2  TrfM=-y/2.0X  12.5=5.  Supposing, 


RADIO    COMMUNICATION. 


217 


for  instance,  that  the  frequency  is  100,000,  the  coils  must  be  so  placed 
that  their  mutual  inductance  is  2^x100-000'  or  7-96  microhenries. 

Current  and  Voltage  Ratios.— The  current  ratio  (secondary  to  pri- 
mary) in  the  high  frequency  transformer,  when  adjusted  to  give 

VET 
^1,  so  that,  in  general,  it 

may  be  increased  by  decreasing  the  secondary  resistance  or  by 
increasing  the  primary  resistance. 


PIG.  152 

KeUTive    values  of  secondary  currents 
L&r&est  v«alue  taKen  AS.  1. 

^ 

s^ 

/ 

N 

f 

\ 

t 

\ 

o    i 

/ 

^. 

^ 

!/ 

•*• 

•~> 

•^ 

/ 

-~ 

~^ 

•^ 

^ 

«•>  f 

/ 

~~ 

^ 

7 

^~  -. 

/ 

7 

<**  fi 

^ 

/ 

I 

15                 S                  ~\5                  »o                ITS                 IS                 n-S             10 

Ztr-f  M 

vAriAtion    of  Secondary  current  with  the  cou^Ii'n^ 

The  voltage  ratio  is  in  general  more  complicated.     If  the  two  cur- 
rents are  tuned  to  one  another  and  to  the  impressed  frequency,  the 

ITT 

voltage  ratio  (secondary  to  primary)  approaches  the  value  -./-^  as  the 

y  ^2 

resistances  in  the  circuits  are  made  smaller.  If  the  circuits  are  not 
tuned  to  the  same  frequency,  but  are  closely  coupled,  the  voltage 
ratio  approaches  the  ratio  of  the  number  of  turns  on  the  two  coils- 
(when  the  resistance  may  be  neglected),  which  is  the  case  of  the  usual 
alternating  current  transformer. 


218  RADIO    COMMUNICATION. 

122.  Free  Oscillations  of  Coupled  Circuits  with  Small  Damping.— 
Suppose  the  condenser  in  the  primary  circuit  is  given  a  charge,  and 
the  primary  circuit  is  closed  directly  or  through  a  spark  gap.  If  the 
secondary  circuit  is  open,  the  primary  will  oscillate  freely,  the  fre- 
quency of  the  current  being  given  by  the  equation  /i  = w=^-,  the 

2irV£1C;, 

damping  of  the  oscillations  being  determined  by  the  ratio  ~ —}r- 

-  JLi 
as  treated  in  Section  116. 

As  soon  as  the  secondary  is  closed,  the  matter  is  complicated 
by  the  reaction  of  each  circuit  upon  the  other.  An  emf .  is  induced 
in  the  secondary  by  the  changes  of  the  primary  current,  and  thereby 
a  forced  oscillation  is  started  in  the  secondary.  The  secondary 
condenser  is  charged  by  this  current  and  starts  a  free  oscillation, 
whose  period  will  depend  on  the  constants  of  the  secondary  circuit. 
This  latter  wave  will  induce  a  forced  oscillation  in  the  primary, 
and  similarly  the  oscillation  which  was  forced  in  the  secondary 
by  the  primary,  will  react  on  the  primary,  modifying  the  original 
oscillation  in  the  primary  which  produced  it.  The  oscillations 
in  the  primary  will  then  further  react  on  the  secondary,  and  so  on. 

Naturally,  the  result  will  be  very  complicated,  but  it  is  evident 
that  each  circuit  is  the  seat  of  two  waves,  one  free  and  the  Other 
forced  by  the  other  circuit.  Each  of  the  waves  which  we  have 
designated  as  free  is,  however,  not  entirely  so,  since  it  forces  an 
oscillation  of  its  own  frequency  in  the  other  circuit,  and  has  to  supply 
the  energy  for  this  induced  wave.  This  has  the  effect  of  modifying 
the  frequencies  of  these  waves  from  the  natural  values  /j  and  /2 
already  treated.  Of  the  two  waves  in  the  primary,  the  free  wave 
has  (with  loose  coupling)  the  greater  amplitude,  and  the  same  is 
true  of  the  secondary  except  that  here  the  amplitudes  of  the  waves 
are  more  nearly  equal.  With  close  coupling,  the  forced  wave  in 
the  primary  becomes  stronger,  owing  to  the  increased  amplitude 
of  the  secondary  free  wave.  Finally,  with  very  close  coupling,  those 
waves  predominate  the  frequency  of  which  is/x.  The  frequency /7/ 
of  the  other  waves  lies  so  far  above  the  natural  frequency  of  either 
circuit  that  only  feeble  oscillations  of  this  frequency  are  present. 

In  general  therefore  the  oscillations  in  both  the  primary  and 
secondary  circuits  are  compounded  of  two  damped  oscillations  of 
different  frequencies.  It  is  of  interest  to  study  a  little  more  closely 
the  nature  of  the  complex  oscillations  resuting  from  the  super- 


RADIO    COMMUNICATION.  219 

position  in  a  single  circuit  of  the  two  oscillations  of  different  fre- 
quencies. 

Damping  Curves  of  Coupled  Circuits. — Fig.  153  shows  two  sine 
waves  A  and  B  of  equal  amplitudes  but  of  different  frequencies. 
Curve  C  is  obtained  by  taking  the  algebraic  sum  of  the  ordinates 
of  A  and  B.  It  is  seen  to  be  a  curve  the  oscillations  of  which  alter- 
nately increase  and  die  away.  The  frequency  of  these  fluctua- 
tions is  equal  to  the  difference  of  the  frequencies  of  the  components 
A  and  B.  The  curve  C  passes  through  its  zero  values  at  nearly 
regular  intervals  of  time,  excepting  at  those  moments  when  the 
resultant  amplitude  is  passing  through  its  minimum,  when  the 
curve  makes  an  additional  passage  through  zero  at  the  moment 
the  resultant  maximum  amplitude  is  zero.  It  is  also  noticeable 
that  the  loops  of  the  curve  C  are  only  approximately  of  sine  shape. 

An  exactly  analogous  case  is  furnished  by  the  resultant  sound 
wave  coming  from  two  tuning  forks  which  are  vibrating  with  some- 


what  different  frequencies.  The  sound  which  is  heard  alternately 
increases  and  decreases  in  loudness,  giving  the  phenomenon  of 
"beats."  The  number  of  beats  per  second  is  equal  to  the  differ- 
ence in  frequencies  of  the  two  forks.  Thus,  if  two  forks  have  fre- 
quencies of  259  and  255  vibrations  per  second,  they  combine  to  give 
a  sound  which  beats  four  times  per  second. 

Free  oscillations  in  coupled  circuits  are  damped,  so  that  in  addi- 
tion to  the  alternate  waxing  and  waning  of  the  resultant  oscillation, 
the  energy  of  the  oscillation  as  a  whole  dies  away  according  to  the 
laws  already  treated  in  Section  116.  Fig.  154  shows  the  nature 
of  the  damped  oscillations  in  the  primary  and  secondary  circuits. 
The  primary  decrement  is  assumed  to  be  0.1  and  that  of  the  secondary 
0.05.  The  two  coexistent  frequencies  are  supposed  to  have  the 
ratio  of  4  to  5.  The  curve  of  oscillations  is  in  each  case  drawn  as  a 
full  line.  The  dotted  curves  show  the  beating  effect  described 
above,  while  the  dashed  curves  give  an  indication  of  the  damping 


220 


RADIO    COMMUNICATION. 


effect.  It  is  noticeable  that  the  primary  current  is  passing  through 
its  maximum  values  at  the  moments  when  the  secondary  current 
is  zero,  and  vice  versa.  Further  when  the  primary  is  passing  through 
a  period  of  intense  oscillation  the  secondary  oscillations  are  small,  etc. 
Another  important  conclusion  which  can  be  drawn  from  Fig.  154 
is  that  the  energy  of  the  coupled  system  is  transmitted  alternately 
from  the  primary  to  the  secondary,  and  back  again  from  the  second- 
ary to  the  primary.  Thus,  at  certain  moments  the  energy  is  en- 
tirely in  the  primary,  at  others  entirely  in  the  secondary,  and  at 
other  instants  partly  in  the  primary  and  partly  in  the  secondary. 


Primary  OstflldTiona 


Oscillations    'in    Couf>l«d  Circuits. 
D«crem«nT  of   Primary  *  o.l 
ecrement  of  Secondary-  o, OS 


Ratio  of 
.___  Secondary    OscilUtioni 

wfl'  TT/KA'A  A^~J\W/ 


This  transfer  of  energy,  first  in  one  direction  and  then  in  the  other, 
shows  that  the  primary  and  secondary  play  alternately  the  role  of 
driving  circuit. 

From  the  standpoint  of  radiation  of  energy,  it  is  desirable  to  hinder 
the  return  of  energy  to  the  primary,  after  it  has  once  been  given  to 
the  secondary.  Since  the  closed  primary  circuit  is  of  such  a  nature 
as  to  radiate  very  little  energy  (see  Sec.  136),  no  useful  purpose  is 
served  by  the  transfer  of  energy  back  to  the  primary,  and  some  of 
the  energy  thus  handed  back  is  necessarily  lost  in  heating  in  the 
primary.  Further,  the  radiation  of  the  energy  of  the  secondary  in 


RADIO    COMMUNICATION.  221 

waves  of  two  different  frequencies  is  undesirable.  The  receiving- 
circuit  can  be  tuned  to  give  a  maximum  of  current  for  either  one  of 
the  incoming  wave  frequencies,  but  not  for  both  at  the  same  time. 
The  partition  of  the  radiated  energy  of  the  secondary  in  waves  of 
two  frequencies  is  therefore  wasteful,  since  only  that  wave  to  which 
the  receiving  circuit  is  tuned  is  effective,  while  practically  none  of 
the  energy  of  the  other  wave  is  usefully  employed,  and  it  may  cause 
interference  with  other  stations. 

123.  Impulse  Excitation.  Quenched  Gap. — If  by  some  means  or 
other,  the  energy  of  the  primary  circuit  can  be  transferred  to  the 
secondary  and  then  all  connection  between  the  circuits  can  be  re- 
moved before  any  energy  can  be  handed  back  to  the  primary,  we 
may  avoid  the  disadvantages  just  mentioned.  In  this  case,  the  sec- 
ondary will  oscillate  simply  in  its  own  natural  frequency,  and  the 
loss  of  energy  in  the  primary  can  be  restricted  to  the  short  interval 
during  which  the  primary  is  acting.  By  properly  choosing  the  re- 
sistance of  the  secondary,  the  damping  of  the  radiated  wave  may  be 
kept  small,  and  since  only  a  single  frequency  is  radiated,  the  advan- 
tages of  close  tuning  of  the  receiving  circuit  can  be  realized.  Such 
a  method  of  excitation  is  known  as  " impulse  excitation,"  and  is 
analogous  to  the  mechanical  case  where  a  body  is  struck  a  single 
sharp  blow,  and  thereafter  executes  vibrations,  the  period  of  which 
depends  entirely  on  the  inertia  and  elasticity  constants  of  the  body- 
itself ,  and  not  at  all  on  the  nature  of  the  body  from  which  the  impulse 
has  emanated. 

One  means  of  obtaining  an  impulse  excitation  of  the  secondary  is 
to  insert  so  much  resistance  in  the  primary  that  its  current  falls  away 
aperiodically  (see  Sec.  116).  This  has,  however,  the  disadvantage 
that  considerable  energy  is  lost  in  the  primary  due  to  the  heating  of 
the  rather  large  resistance  of  the  primary  by  the  initially  rather  large 
primary  current.  A  more  satisfactory  arrangement  is  the  ' '  quenched 
gap."  By  dividing  the  spark  gap  in  the  primary  into  a  number  of 
short  gaps  in  series,  the  cooling  effect  of  the  relatively  large  amount 
of  metal  is  available  for  carrying  away  the  heat  of  the  spark  dis- 
charge. This  is  found  to  be  sufficient,  in  the  case  of  a  properly  de- 
signed quenched  gap,  to  prevent  the  reestablishmeno  of  a  spark  dis- 
charge after  the  first  passage  of  the  primary  oscillations  through  their 
condition  of  maximum  amplitude  to  zero,  as  at  point  Z),  Fig.  154.  The 
secondary,  at  this  moment,  is  the  seat  of  the  whole  of  the  energy  of 
the  system  and  thereafter  oscillates  at  the  single  frequency  natural 


222 


RADIO   COMMUNICATION. 


to  it.  The  damping  of  the  primary  does  not  have  to  be  made  excess- 
ive, and  the  energy  lost  in  the  primary  is  restricted  to  the  heating 
during  the  short  interval  before  the  quenching  of  the  primary  oscil- 
lations. 

Fig.  155  shows  the  form  of  the  oscillations  in  the  two  circuits 
for  this  case.     The  curves  are  tho  same  as  in  Fig.  154  up  to  point  D, 


Quenched    Primary  OscilUT 


FlQ     155 

Oscillations  of  Glue.nc.hed 
Cja|3    Girouits 

Pri 
Se 


Osci  I  Uti'ons 


after  which  the  secondary  curve  is  a  simple  feebly  damped  oscilla- 
tion. The  construction  and  operation  of  the  quenched  gap  are 
treated  further  in  Chapter  5,  Section  156. 


CHAPTER  4. 

ELECTROMAGNETIC  WAVES. 
A.  Wave  Motion. 

124.  Three  Ways  of  Transmitting  Energy. — All  of  the  ways  of 
signaling  between  distant  places  operate  by  one  or  by  a  combination 
of  these  three  methods: 

(a)  By  a  push  or  pull  on  something  connecting  the  two  places. 

(6)  By  projectiles. 

(c)  By  wave  motion. 

Thus  think  of  all  the  ways  in  which  you  can  arouse  a  dog  asleep 
at  the  other  side  of  the  room.  You  can  prod  him  with  a  long  stick 
(method  a}.  You  can  throw  something  at  him;  if  you  hit  him  it  is  a 
case  of  method  6;  if  you  miss  him,  the  noise  made  when  the  missile 
hits  the  wall  or  floor  may  wake  him,  in  which  case  we  have  a  com- 
bination of  methods  b  and  c.  You  can  whistle  or  call  (method  c). 
You  can  flash  a  light  in  his  eyes  (method  c).  Any  way  that  you  can 
think  of  is  an  example  of  one  of  these  three  methods.  Of  the  three 
methods  the  most  important  for  our  purpose  is  the  third. 

125.  Properties    of   Wave    Motion. — Everyone   is   familiar  with 
water  waves.     Many  of  their  properties  are  common  to  all  kinds  of 
waves.     Thus  the  alternate  crests  and  hollows,  though  invisible  in 
many  types  of  waves  are  present  in  all.     Examples  of  different 
wave  shapes  are  shown  in  Figs.  80  and  95,  Chapters  1  and  2.     The 
simplest  wave  shape  is  the  sine  wave  (Fig.  80). 

Also,  as  in  the  case  of  water  waves,  all  waves  have  a  definite 
wave  length  X,  which  is  the  distance  between  successive  crests  or 
successive  hollows.  If  we  use  the  term  phase  to  mean  the  position 
at  any  time  of  a  point  on  the  wave  outline,  we  can  say  that  in  general 
the  wave  length  is  the  distance  between  two  successive  points  in 
the  same  phase. 

Furthermore,  waves  of  all  kinds  travel  with  a  definite  velocity. 
If  one  looks  at  a  fixed  point  on  the  surface  of  a  pool  over  which 
ripples  are  moving,  he  can  see  that  a  crest  appears  at  that  point  a 

223 


224  RADIO  COMMUNICATION. 

definite  number  of  times  in  any  given  interval  of  time.  The  number 
so  appearing  in  one  second  is  called  the  frequency,  /.  If  now  the 
frequency  is  multiplied  by  the  length  of  one  wave,  we  get  the 
distance  moved  by  the  waves  in  one  second,  which  is  the  velocity,  c, 
or,  in  symbols,  c=X/.  The  velocity  of  waves  of  different  kinds  is 
very  different  in  amount.  Thus  ripples  on  water  travel  with 
velocities  of  from  10  to  100  cm.  per  second;  for  sound  waves  in  air 
the  velocity  is  330  meters  per  second ;  and  the  velocity  of  light  and 
electric  waves  is  300,000,000  meters  per  second.1 

The  more  the  surface  of  the  water  is  displaced  by  the  waves  from 
its  position  of  rest,  the  greater  is  the  amount  of  energy  being  passed 
along.  The  amount  of  energy  transmitted  by  water  waves  is  con- 
nected with  the  height  of  the  crests  and  the  depth  of  the  troughs. 
This  also  is  true  of  all  kinds  of  waves.  The  greatest  displacement 
from  the  position  of  rest  that  any  point  undergoes  is  called  the 
''amplitude"  of  the  wave.  Thus  we  say  that  the  energy  in  wave 
motion  depends  upon  the  amplitude.  The  amount  of  energy  in  the 
wave  depends  on  the  work  which  has  to  be  done  to  produce  the 
displacement.  This  is  in  general  equal  to  the  product  of  the  resisting 
force  and  the  distance  moved.  Now  in  the  case  of  many  kinds  of 
waves,  including  electric  waves,  the  resisting  force  is  proportional 
to  the  distance  moved.  Hence  the  work  done  and  the  energy 
transmitted  is  proportional  to  the  square  of  the  amplitude  of  the 
wave. 

126.  Wave  Trains,  Continuous  and  Discontinuous. — If  a  stone  is 
dropped  into  a  quiet  pool  of  water,  a  "train"  of  waves  is  started 
which  soon  passes  out  from  the  starting  point  in  all  directions,  leav- 
ing the  surface  behind  it  undisturbed.  If  a  second  stone  is  dropped 
just  at  the  moment  that  the  surface  at  the  starting  point  has  com- 
pleted one  up-and-down  excursion,  another  wave  train  will  start  in 
phase  with  the  first,  and  the  two  will  form  one  train.  If  the  process 
is  repeated  once  after  each  complete  vibration  of  the  surface  at  the 
starting  point,  continuous  waves  are  produced.  Similarly,  if  we 
hold  a  vibrating  body  so  that  it  touches  the  surface,  continuous 
waves  are  produced.  By  interrupting  the  vibrations  of  the  body, 
we  can  produce  interrupted  or  discontinuous  trains  of  waves. 

*  Example.— What  is  the  wave  length  of  waves  having  a  frequency  of  100,000  cycles 
per  second  which  travel  with  a  velocity  of  300,000,000  meters  per  second, 
c 


X  = 


/  ~~     100,000 


RADIO   COMMUNICATION.  225 

Examples  of  these  two  kinds  of  wave  trains  are  met  with  often. 
Thus  the  sound  from  a  musical  instrument  where  the  strings  are 
set  in  vibration  by  picking  (as  with  a  mandolin)  is  transmitted  in 
discontinuous  trains,  while  that  from  an  instrument  whose  strings 
are  bowed  (as  a  violin)  is  transmitted  by  more  nearly  continuous 
waves.  Similarly,  in  radio  we  have  to  do  with  both  kinds,  contin- 
uous waves  being  furnished  by  high  frequency  alternators,  the 
Poulsen  arc,  and  the  oscillating  vacuum  tube,  while  discontinuous 
trains  are  given  by  condenser  discharges  in  spark  circuits.  In 
these  latter  the  amplitude  of  the  waves  diminishes  steadily  in  each 
wave  train;  these  are  called  "damped"  waves.  Such  waves  are 
discussed  in  Section  115. 

B.  Propagation  of  Waves. 

127.  Waves  Propagated  by  Elastic  Properties  of  Medium.1 — In 

the  case  of  ripples  on  the  surface  of  water  it  is  plain  to  the  eye  that 
the  waves  are  transmitted  by  the  passing  on  of  the  up-and-down 
motion  of  the  surface  at  the  source.  This  is  possible  because  at  the 
surface  of  the  water  the  particles  of  the  water  are  held  together  by 
forces  which  resist  their  displacement.  When  one  particle  is  dis- 
placed, its  neighbors  are  dragged  with  it  to  some  extent.  In  tech- 
nical terms,  the  medium  of  transmission  is  said  to  have  "elastic" 
properties  and  the  forces  brought  into  play  are  said  to  be  elastic 
forces.  The  velocity  of  the  waves  (ripples)  depends  on  the  nature 
and  amount  of  these  elastic  forces. 

In  the  case  of  sound  waves  in  air,  we  do  not  ordinarily  see  the 
vibrations  of  the  particles  of  the  air.  The  vibrations  are  quite  small 
and  the  waves  travel  so  fast  that  only  under  quite  unusual  conditions 
can  they  be  made  visible.  But  the  mechanism  by  which  the  energy 
is  transmitted  is  found  to  be  of  the  same  kind  as  in  the  case  of  water 
ripples.  By  the  delicate  elastic  connections  between  neighboring 
portions  of  the  air  a  vibration  at  one  point  is  passed  on  to  another. 
Sound  waves  are  of  another  type  than  water  waves  only  because 
the  structure  of  air  is  different  from  that  of  water.  Hence  the  elastic 
reaction  to  displacement  is  different  in  the  two  media.  This  is  the 
sole  cause  of  the  differences  between  any  two  types  of  waves. 

128.  Properties  of  Electromagnetic  Waves.— In  the  case  of  electro- 
magnetic waves,  often  called  "electric  waves,"  the  displacements 
produced  are  of  the  kind  already  considered  in  the  section  on  capaci- 

1  For  further  explanation  of  the  radiation  of  electric  waves,  see  Starling,  "  Elec- 
tricity and  Magnetism,"  pp.  423-429. 
97240°— 19 15 


226 


RADIO   COMMUNICATION. 


tance  (Sec.  2J).  The  elastic  reactions  set  up  by  such  displacement 
currents  can  be  found  by  the  same  laws  which  determine  the  electric 
and  magnetic  forces  due  to  any  current.  It  is  beyond  the  scope  of 
this  book  to  show  the  nature  of  these  electrical  elastic  forces.  It 
will  be  sufficient,  however,  to  state  that  they  are  such  as  to  produce 
waves  in  which  (in  free  space,) — 

(a)  The  displacement  (and  the  electric  field  intensity)  are  at 
right  angles  to  the  direction  of  motion  of  the  wave  train. 

(&)  The  magnetic  field  intensity  resulting  from  the  displacement 
current  is  at  right  angles  to  the  displacement  and  to  the  direction  of 
the  wave  train. 

(c)  The  variations  in  the  displacement  (or  the  electric  field  inten- 
sity) and  the  magnetic  field  intensity  are  in  phase. 


Electric  lines   of  force 


The  «lectri'c  field  And  the  magnetic        charged     ^late.   condenser 
•field  are  A?  ri>,hT  angles  .and  travel 


toiefher. 


(d)  The  velocity  of  the  waves  is  3  X  108  meters  per  second,  the 
same  as  the  velocity  of  light. 

These  relations  are  shown  in  Fig.  156,  where  the  curve  marked 
E  or  D  shows  the  variations  in  the  electric  field  intensity  or  displace- 
ment, and  that  marked  H  the  variations  in  the  magnetic  field  inten- 
sity, the  wave  moving  in  the  direction  shown  by  v. 

129.  Modification  of  Waves  in  Free  Space  Near  the  Earth. — Such 
waves  if  started  at  a  point  in  free  space  travel  in  all  directions  with 
the  same  velocity.  They  may  be  modified  in  various  ways  as  they 
proceed.  Thus,  if  they  pass  into  a  region  of  different  dielectric 
constant,  they  are  in  general  changed  slightly  in  direction  and 
partly  reflected.  Their  energy  is  also  absorbed  to  a  greater  or  less 


RADIO    COMMUNICATION.  227 

extent  in  their  passage  through  any  medium.  This  absorption  is 
greater  for  short  than  for  long  waves.  In  a  perfect  conductor  no 
waves  could  be  transmitted,  since  in  such  a  medium  there  is  no 
elastic  opposition  to  the  displacement  of  electricity.  A  perfectly 
conducting  sheet  would  reflect  all  of  the  wave  energy  falling  on  it. 
However,  a  conductor  parallel  to  the  direction  of  motion  of  a  wave 
acts  as  a  guide  to  the  wave,  through  the  action  of  currents  induced 
in  it  by  the  varying  magnetic  field  of  the  wave.  It  takes  less  energy 
from  the  waves,  the  better  conductor  it  is.  In  the  use  of  electric 
waves  in  radio  communication,  all  of  these  modifications  occur  and 
serve  to  explain  many  of  the  irregularities  of  received  signals.  We 
can  think  of  the  space  through  which  radio  signals  are  sent  as  being 
bounded  below  by  a  sheet  of  varying  conductivity  (the  earth's 
surface)  and  above — at  a  distance  of  from  30  to  50  miles — by  another 
conducting  region.  This  upper  region  where  the  air  is  much  rarefied 
is  a  fairly  good  conductor,  owing  to  its  ionization  by  radiations  from 
the  sun.  The  region  in  between  these  conducting  layers  is  usually 
a  good  dielectric.  Thus,  this  region  acts  more  or  less  as  a  speaking 
tube  does  for  sound  waves,  though  its  action  is  much  more  compli- 
cated. The  electromagnetic  waves  are  set  up  near  the  earth's 
surface.  They  are  partly  transmitted  as  guided  wave  trains  along 
the  earth's  surface,  modified  by  refractions  and  absorption  at  its 
irregularities;  another  part,  however,  goes  off  as  space  waves,  which 
by  reflections  at  the  upper  and  lower  layers  of  the  conducting  bound- 
aries may  recombine  with  the  guided  wave  in  such  a  way  as  either 
to  add  or  subtract  their  effects,  depending  on  circumstances.  In 
the  daytime  the  upper  conducting  boundary  will  be  less  definitely 
marked  than  at  night,  on  account  of  partial  ionization  of  the  air  by 
the  sun's  radiations.  Hence,  there  will  be  less  reflection  of  the  space 
wave  in  the  daytime,  and  consequently  the  guided  wave  will  pro- 
duce the  greater  part  of  the  effect  at  the  receiving  station.  In  the 
night,  however,  when  the  upper  boundary  is  more  sharply  defined, 
there  is  more  reflection  of  the  space  wave,  and  in  general  signals 
received  at  night  are  stronger  than  in  daytime.  Night  signals  are, 
however,  more  variable  in  intensity,  particularly  for  short  waves. 
This  is  especially  true  during  the  time  when  the  sunset  line  is  passing 
between  two  communicating  stations.  This  is  in  general  what  we 
should  expect,  as  the  upper  boundary  would  be  quite  variable  under 
such  circumstances.  Clouds  and  other  meteorological  conditions 
would  cause  great  variations  in  the  sharpness  of  this  boundary  sur- 


228  RADIO  COMMUNICATION. 

face,  and  this  may  explain  the  rapid  fluctuations  in  the  strength  of 
received  signals  often  observed. 

From  all  these  considerations  it  can  be  seen  that  the  conditions 
under  which  received  signals  will  be  most  uniform  in  intensity  are: 

(a)  Transmission  using  long  waves. 

(6)  Transmission  by  daylight. 

(c)  Transmission  over  short  distances. 

(d)  Transmission  over  uniform  conducting  surface  of  sea  water. 

It  is  only  under  these  conditions  that  the  performance  of  different 
transmitting  stations  can  be  fairly  compared. 

130.  Static. — The  transmission  of  signals  by  electromagnetic 
waves  is  often  interfered  with  by  stray  waves  and  static  charges  called 
"strays"  or  "atmospherics,"  which  give  rise  to  variable  currents  in 
the  receiving  antennas.  These  cause  troublesome,  interfering  sounds 
of  a  harsh,  irregular  nature  in  the  radio  receiver.  These  effects  are 
most  frequent  in  summer  and  especially  in  a  thunderstorm.  They 
are  often  very  pronounced  when  a  thunderstcrm  is  a  few  miles  away. 
They  appear  to  be  of  two  kinds;  (a)  charges  of  electricity  which  come 
from  the  surrounding  atmosphere  upon  the  antenna  and  then  dis- 
charge to  ground  producing  a  current;  and  (6)  electromagnetic  waves 
which  are  produced  by  distant  lightning  or  other  electromagnetic 
disturbance  in  the  atmosphere.  Strays  are  the  worst  enemy  of  radio 
communication,  especially  in  tropical  countries.  No  satisfactory 
method  of  eliminating  them  has  been  devised.  They  are  much  re- 
duced by  taking  certain  precautions.  One  is  the  use  of  loose  coup- 
ling between  the  receiving  antenna  and  detecting  circuit.  Another 
is  the  use  of  waves  of  zero  or  small  decrement  and  receiving  appara- 
tus which  can  be  very  sharply  tuned.  The  use  of  a  musical  note  in 
the  transmitted  signals  also  helps  to  overcome  disturbance  from  strays. 
Strays  have  been  found  in  some  cases  to  be  reduced  by  using  small 
antennas  or  closed  coil  receiving  aerials,  with  amplifiers.1 

C.  Theory    of    Production    and    Reception    of    Electromagnetic 

Waves. 

To  produce  a  train  of  waves  of  any  kind,  a  vibrating  body  is  neces- 
sary. The  vibrations  of  this  body  have  next  to  be  communicated  to  a 
continuous  medium,  after  which  the  elastic  properties  of  the  medium 

1  Information  on  strays  and  special  methods  of  overcoming  them  is  given  in  Flem- 
ing, "  Electric  Wave  Telegraphy  and  Telephony,"  3d  ed.,  pp.  774, 851,  and  Goldsmith, 
"Radio  Telephony,"  p.  220. 


RADIO    COMMUNICATION.  229 

take  care  of  the  transmission  of  the  waves.  In  the  case  of  electro- 
magnetic waves  the  vibrating  body  is  an  oscillating  electric  charge 
in  a  circuit  (the  sending  antenna  circuit),  while  the  means  by  which, 
these  oscillations  are  communicated  to  free  space  can  best  be  de- 
scribed in  terms  of  the  motion  of  the  lines  of  force  which,  when 
at  rest,  are  used  to  picture  the  field  about  electric  charges  as  in. 
Fig.  53. 

These  lines  are  to  be  looked  at  as  lines  along  which  there  is  a  dis- 
placement of  electricity  against  the  elastic  force  of  the  medium. 
Thus  they  cannot  exist  in  conductors  (in  which  no  such  elastic  forces; 
exist).  Under  the  action  of  the  elastic  forces  the  displaced  elec- 
tricity is  continually  urged  to  return  to  its  position  of  rest.  In  other 
words,  there  is  a  tension  along  the  lines  of  force.  In  addition  there 
must  be  a  pressure  at  right  angles  to  the  lines  of  force,  otherwise  those 
lines  would  always  be  straight  and  parallel  under  the  action  of  the 
tensions.  These  pressures  can  be  thought  of  as  arising  from  the  re- 
pulsion between  the  displaced  charges  of  the  same  sign  in  neighbor- 
ing lines. 

131.  Magnetic  Field  Produced  by  Moving  Lines  of  Electric  Dis- 
placement.— Consider  what  happens  to  the  lines  of  force  when  a. 
condenser  is  discharged.  Before  the  discharge  begins,  the  field  is  as 
shown  in  Fig.  157.  Now,  suppose  a  wire  to  replace  the  line  abc, 
thus  discharging  the  condenser.  The  displacements  previously 
existing  along  abc  vanish,  or,  in  other  words,  the  line  shrinks  to  noth- 
ing when  the  tension  is  relieved.  But  this,  at  the  same  time,  does, 
away  with  the  sidewise  pressure  on  the  neighboring  lines,  which  as 
the  pressure  from  the  lines  outside  of  them  still  remains,  move  inward 
toward  the  wire  under  the  action  of  this  unbalanced  pressure.  Their 
ends  slide  along  the  plates  of  the  condenser  during  this  motion  and 
when  they  come  to  the  wire  the  displacements  along  their  length 
vanish.  This  process  continues  until  all  the  lines  have  vanished, 
and  the  condenser  is  discharged. 

Now,  while  this  is  happening  to  the  electric  lines  of  force  in  the- 
field,  a  current  has  been  flowing  in  the  condenser  plates  and  the  wire 
abc;  also  the  magnetic  lines  of  force  which  always  accompany  any 
current  have  sprung  into  existence  and  continue  to  exist  as  long  as. 
the  current  flows.  In  the  space  between  the  condenser  plates,  these 
magnetic  lines  of  force  will  be  directed  up  from  the  plane  of  the  paper 
at  right  angles,  both  to  the  electric  lines  of  force  and  to  the  direction, 
of  their  motion.  These  two  facts  can  be  described  in  terms  of  the 


230 


RADIO  COMMUNICATION. 


motion  of  the  lines  by  saying  that  the  motion  of  the  ends  of  the  elec- 
tric lines  along  a  conductor  causes  a  current  to  flow  in  it,  while  the 
motion  of  the  electric  lines  at  right  angles  to  their  own  length  pro- 
duces magnetic  lines  of  force  in  the  other  direction,  which  is  per- 
pendicular to  the  direction  of  motion.  If  the  motion  of  the  electric 
line  is  parallel  to  its  length,  there  will  be  no  magnetic  field  pro- 
duced. From  this  point  of  view,  what  takes  place  in  the  medium 
is  the  cause  of  what  takes  place  in  conductors.  The  energy  in  the 
former  (in  the  case  we  are  considering)  appears  in  the  latter  as  heat. 
132.  Mechanism  of  Radiation  from  a  Simple  Oscillator.— Now 
consider  what  takes  place  when  the  discharge  is  oscillatory  instead 
of  in  one  direction.  To  fix  our  ideas,  let  us  take  the  case  of  the  simple 


FIG  tsa 


Hertzian  oscillator,  the  electrostatic  field  of  which,  before  the  gap 
becomes  conducting,  is  shown  in  Fig.  158-a.  (The  field  to  the  left 
is  shown  by  dotted  lines,  in  order  to  be  able  to  keep  track  of  each 
line  clearly  in  its  motion  as  shown  in  the  following  figures.)  When 
a  spark  passes  and  the  gap  becomes  conducting,  the  electric  line  of 
force  ab  vanishes  and  those  from  each  side  begin  to  move  up  under 
the  unbalanced  sidewise  pressure,  as  before.  Here,  however,  when 
the  ends  of  the  line  abc  reach  the  gap,  we  must  suppose  that  it  has 
sufficient  momentum  so  that  the  ends  cross  and  the  middle  portion 
travels  across  the  gap.  After  two  lines  have  done  this,  the  state  of 
things  is  as  represented  in  Fig.  158-b.  There  will  soon  come  a 
different  state  of  things,  however,  owing  to  the  shape  of  the  lines. 


RADIO    COMMUNICATION.  231 

When  tho  ends  get  to  the  gap  before  the  middle  portion,  as  shown  in 
Fig.  158-c,  they  will  cross  as  before,  and  soon  thereafter  we  will  have 
the  loop  formed  as  in  Fig.  158-d.  Now,  at  some  time  as  the  ends 
continue  to  go  up,  this  loop  will  break,  forming  two  parts  m  and  n, 
as  shown  in  Fig.  158-e.  This  is  because  at  that  moment  the  angle 
of  intersection  becomes  so  acute  that  each  part  of  the  line  will  be 
moving  parallel  to  its  length,  in  which  case  neither  half  will  have 
any  magnetic  field  and,  consequently,  no  momentum  to  carry  them 
by  each  other.  The  process  goes  on  as  shown  in  Figs.  158-f ,  g,  and 
h,  the  last  of  which  shows  the  state  of  things  when  one  half  oscillation 
has  been  completed,  and  the  charges  on  the  oscillator  have  been 
reversed  in  sign.  A  cylindrical  sheet  of  lines  of  force  has  then  been 
detached  from  the  oscillator  and  is  traveling  outward.  At  this 
moment  those  lines  left  attached  to  the  oscillator  have  been  stretched 
as  far  as  their  momentum  can  carry  them,  and  they  begin  to  con- 
tract again  and  repeat  the  process,  provided  the  gap  is  still  conduct- 
ing. In  the  next  half  wave  length,  another  cylindrical  sheet  of  lines 
of  force  will  be  snapped  off,  so  to  speak,  and  the  process  will  continue 
until  the  energy  lost  as  heat  in  the  oscillator  has  exhausted  the  supply 
of  lines  which  remain  attached  to  it.  These  cylindrical  sheets,  as 
they  spread  out,  become  more  and  more  nearly  plane,  the  plane  being 
perpendicular  to  the  motion  away  from  the  oscillator.  During  the 
process  shown  in  Figs.  158-b  to  158-g,  that  is,  while  the  current  in 
the  oscillator  is  flowing  upward,  the  motion  of  the  electric  lines  of 
force  generate  magnetic  lines  (not  shown),  which  form  circles  around 
the  oscillator  running  into  the  paper  to  the  right  and  coming  out  on 
the  left.  These  magnetic  lines  vanish  at  any  point,  when  the  electric 
lines  of  the  attached  field  come  to  rest  as  in  Figs.  158-a  or  158-h,  but 
continue  with  the  moving  electric  lines  of  the  radiated  cylindrical 
sheet.  When  the  cylindrical  sheets  have  moved  so  far  that  they  can 
be  considered  practically  as  planes,  then  the  magnetic  lines  also  lie 
in  these  planes,  but  perpendicular  to  the  electric  lines  and  to  the 
direction  of  motion. 

In  the  case  of  a  simple  vertical  antenna,  the  mechanism  of  radia- 
tion is  quite  similar.  In  this  case,  however,  since  the  lower  end 
of  the  antenna  is  earthed,  only  the  upper  halves  of  the  waves  shown 
in  Figs.  158-a  to  158-h  are  produced,  so  that  the  field  looks  like 
that  shown  in  Fig.  159,  where  the  electric  lines  are  shown  in 
elevation  and  the  magnetic  lines  in  plan,  while  in  between  is  shown 
the  wave  form  common  to  both.  At  any  one  point  in  space,  the 


232 


RADIO   COMMUNICATION. 


lines  approach  and  separate  like  a  bellows.  When  the  wave  has 
progressed  so  far  that  the  lines  can  be  regarded  as  sections  of  planes, 
the  state  of  things  will  be  as  shown  in  Fig.  160  for  the  electric 
lines,  while  the  same  figure  will  also  represent  the  magnetic  lines 
if  rotated  through  90°  about  the  line  ox.  Where  the  surface  over 
which  the  waves  travel  is  not  a  perfect  conductor  the  ends  of  the 
lines  will  be  as  shown  in  Fig.  161. 

The  same  method  of  picturing  the  process  of  wave  production 
applies  to  other  forms  of  radiating  systems  of  either  the  open  antenna 


FlO.159 


Elee-tric.  ^rvd   M&^netic.   Fie-ldi 
Vertical     Wire   Antenna 


or  the  closed  coil  type  (see  Sec.  151).  In  all  forms  loops  are  formed, 
and  detached  in  the  same  general  way.  In  some  of  them  the  dis- 
tribution of  the  lines  of  force  is  such  as  to  favor  the  production  of 
more  such  loops  than  in  others;  this  means  that  such  an  antenna 
will  be  a  better  radiator  than  the  others. 

133.  Action  in  Receiving. — The  mechanism  of  the  reception  of 
•waves  by  an  antenna  can  be  followed  through  in  terms  of  the  lines 


RADIO   COMMUNICATION. 


233 


of  force  in  an  analogous  manner.  Thus  suppose  the  antenna  to  be 
located  with  respect  to  the  incoming  wave  train  as  shown  in  Fig. 
162.  Then  the  upper  ends  of  the  lines  as  they  arrive  travel  down 
the  antenna  as  shown  in  the  dotted  lines  and  give  rise  to  moving 
charges  of  electricity  in  the  antenna,  or  the  receiving  action  can 
be  thought  of  in  another  way.  As  the  advancing  waves  sweep 
across  the  receiving  antenna  the  electric  field  intensity  along  the 
antenna  alternates  in  value.  This  is  equivalent  to  an  alternating 
voltage  between  the  top  of  the  antenna  and  the  ground.  A  still 
different  way  of  looking  at  the  receiving  action  depends  upon  the 
principle  that  an  emf.  is  induced  in  a  conductor  whenever  there  is 
relative  motion  between  the  conductor  and  a  magnetic  field.  The 


Pica, 


Distortion  of  E-lectric.  Lines  ef  Force  in 
Plane  wave  Traveling  overan 
conducting  surface 


tric    Lines  of   Force  in < 
electnc.  wave, 


Electric,    tines   of 
VarTi'oa.1    AnTe.no* 


moving  wave  has  a  magnetic  field  which  sweeps  past  the  antenna, 
and  thus  there  is  relative  motion  between  the  antenna  and  this 
magnetic  field,  which  results  in  an  emf.  in  the  antenna.  This 
emf.  is  what  causes  the  received  current  in  the  antenna. 

The  reception  of  electromagnetic  waves  in  a  closed  coil  used 
in  place  of  an  antenna  can  be  explained  by  the  same  principles. 
The  explanation  is  somewhat  difficult  because  of  the  differences 
of  phase  between  those  currents  in  different  parts  of  the  coil.  For 
such  antennas  it  is  more  convenient  to  think  of  the  current  as  pro- 
duced by  the  changing  magnetic  flux  through  the  coil,  due  to  the 
alternations  of  the  magnetic  field  associated  with  the  wave.  Either 
way  of  looking  at  it  leads  to  the  same  result. 


234  RADIO   COMMUNICATION. 

D.  Transmission  Formulae. 

134.  Statement  of  Formulae.  —  When  the  general  ideas  of  wave 
production  and  reception  discussed  above  are  put  into  exact  mathe- 
matical language,  it  is  possible  to  deduce  certain  practically  useful 
formulae  connecting  the  currents  in  the  sending  and  receiving 
antennae,  their  heights,  resistances,  and  distance  apart.  While  it 
is  beyond  the  scope  of  this  book  to  derive  them,  they  are  given 
without  proof  to  aid  the  student  in  gaining  an  idea  of  the  magnitude 
of  the  effects  to  be  expected  at  various  distances  and  with  different 
types  of  antennae.  In  the  formulae  which  follow  h  stands  for  the 
height  of  an  antenna  or  coil,  /  for  current,  X  for  wave  length,  d  for 
the  distance  apart  of  the  two  antennae  or  coil  aerials,  while  the 
subscripts  s  and  r  refer  to  the  sending  and  receiving  ends,  respec- 
tively. R  stands  for  the  resistance  of  the  receiving  circuit.  All 
lengths  are  supposed  to  be  in  meters. 

If  the  waves  are  sent  out  by  a  simple  flat  top  antenna  and  received 
on  a  similar  one,  we  have 

(83) 

If  the  waves  are  sent  out  by  a  simple  antenna  and  received  on  a. 
closed  coil,  we  have 


where  lr  is  the  length  of  the  receiving  coil  and  NT  the  number  of 
turns  of  wire  with  which  it  is  wound. 

If  the  waves  are  sent  out  by  a  closed  coil  and  received  on  a  simple 
antenna,  we  have 

1184ft,  Zs  hT  Ns  IK 
*  RVd 

where  Zs  is  the  length  of  the  sending  coil  and  Ns  the  number  of  turns 
of  wire  with  which  it  is  wound. 

If  the  waves  are  sent  out  by  a  closed  coil  and  received  on  a  similar 
one,  we  have 

lr  Ns  NT  I3 


In  all  of  these  formulae,  if  d  is  greater  than  100  kilometers,  they 
must  be  multiplied  by  ths  factor  e—  0.000047  -p.  in  order  to  get 

V  x 


RADIO   COMMUNICATION.  235 

more  accurate  results.     (Both  d  and  X  are  in  meters,  and  e  is  equal 
to  2. 718.) 

135.  Examples  of  Use. — To  illustrate  the  use  of  the  formulae 
suppose  it  is  desired  to  know  how  much  current  must  be  put  into  a 
plain  antenna  20  meters  high  sending  a  300-meter  wave,  in  order  that 
the  current  in  a  similar  antenna  50  km.  away  shall  be  detectable 
easily  with  a  crystal  detector  (that  is,  shall  be  about  1/10, 000  amp.), 
the  resistance  of  the  receiving  antenna  being  10  ohms. 

Solving  the  first  equation  for  Js,  we  have: 

T       R\dIT      10X300X50,OOOX-nrfoTr 
J*=1887rfr  188X20X20  = 

As  another  example,  suppose  that  the  receiving  antenna,  in  the 
first  example,  is  replaced  by  a  square  coil  of  2  ohms  resistance,  having 
sides  2  meters  long  and  wound  with  10  turns  of  wire.  If  the  sending 
current  is  £  amp.  as  before,  what  will  be  the  current  in  the  receiving 
coil?  Using  the  second  formula 

1184  ft.  hr  lr  Nr  J.     1184X20X2X2X10XJT    »  -,  /in5 
ir~          R\~d  ~  2X300X300X50,000  —^•i/i()  amp. 

For  a  current  of  this  size  it  would  be  best  to  use  a  simple  vacuum 
tube  receiver  instead  of  a  crystal  detector. 

Asa  third  example,  suppose  the  sending  aerial  to  consist  of  a  single 
square  turn  of  wire  10  meters  on  a  side,  in  which  the  current  is  ^  amp. 
at  X=1000  meters.  With  how  many  turns  should  a  square  coil 
2  meters  on  a  side  and  having  a  resistance  of  5  ohms  be  wound  to 
receive  at  a  distance  of  50  km.,  if  a  vacuum  tube  which  can  detect 
a  current  of  1/108  amp.  is  used?  Solving  the  fourth  equation  for  Nr 
we  have 

Ar  R  x" d  T*  5X109X5X104X1/108 

JVr~7450  h,  ls  ht  I,  Ns  /s~7450X10X10X2X2XlXf~' 

136.  General  Deductions. — From  the  formulae   certain  general 
conclusions  can  be  drawn.    Thus  since  X  appears  in  the  denominator, 
it  folio \vs  that,  for  given  heights  of  antennae,  sending  current,  re- 
ceiver resistance,  and  distance  apart,  there  will  be  more  current  in 
the  receiver,  the  shorter  the  wave  length  used.     On  the  other  hand, 
there  is  more  absorption  of  short  waves  than  long  ones,  as  was  stated 
when  we  were  considering  the  modifications  that  free  waves  undergo 
(Sec.  129).     This  effect  is  taken  account  of  in  the  correction  factor 


236  RADIO   COMMUNICATION. 

to  be  used  for  large  distances.  In  this  factor,  X  enters  in  such  a  way 
as  to  make  the  received  current  less  when  the  wave  length  is  short 
than  when  it  is  long.  Hence,  in  general,  we  conclude  that  to  get 
the  greatest  possible  received  current,  we  should  use  short  waves 
for  short  distances  and  long  waves  for  long  distances. 

It  may  be  seen  from  the  formulae  that,  for  simple  antennae,  the 
received  current  (for  a  given  wave  length,  sending  current,  receiver 
resistance,  and  distance  apart)  is  greater,  the  greater  the  heights  of 
the  antennae.  In  the  case  of  closed-coil  aerials  under  the  same  con- 
ditions, the  received  current  is  greater  the  larger  the  areas  and  the 
number  of  turns  of  the  coils.  For  the  dimensions  actually  used, 
antennae  are  much  more  effective  radiators  and  receivers  than 
closed  coils.  In  order  to  secure  the  same  radiation  or  received 
current  with  a  closed  coil  as  with  an  antenna,  other  conditions  being 
the  same,  its  dimensions  must  be  made  nearly  as  great  as  the  antenna 
height.  However,  it  is  often  possible  to  put  more  current  into  a 
transmitting  coil  than  into  the  corresponding  antenna,  and  also  the 
resistance  of  a  receiving  coil  is  usually  smaller  than  that  of  the  cor- 
responding receiving  antenna.  Hence  the  closed  coil  can  be  a 
smaller  structure  than  the  antenna. 

The  closed  coil  has  some  other  advantages.  For  a  given  power 
input  in  the  transmitter,  the  closed  coil  aerial  is  not  at  quite  such  a 
disadvantage  with  the  ordinary  antenna  as  the  formulae  show, 
because  a  larger  fraction  of  the  radiation  is  sent  out  in  the  direction 
desired.  As  a  receiver,  the  closed  coil  has  the  very  great  advantage 
that  the  direction  of  the  waves  it  receives  can  be  determined. 
These  points  are  discussed  further  in  the  next  chapter. 

E.  Device  for  Radiating  and  Receiving  Waves. 

137.  Description  of  the  Antenna. — The  antenna  is  used  in  radio 
communication  for  two  purposes,  (1)  to  radiate  electric  waves,  and 
(2)  to  receive  or  detect  electric  waves  which  come  to  it.  An  antenna 
consists  essentially  of  one  or  more  wires,  suspended  at  some  elevation 
above  the  earth.  When  electric  waves  reach  an  antenna,  they  set 
up  an  alternating  emf.  between  the  wires  and  the  ground,  and  the 
longer  and  higher  the  wires,  the  greater  the  emf.  produced.  As  a 
result  of  this  emf.,  an  alternating  current  will  flow  in  the  antenna 
wires.  The  energy  of  the  current  is  absorbed  from  the  passing 
wave,  just  as  some  of  the  energy  of  a  water  wave  is  used  up  in  causing 
vibrations  in  a  slender  reed  which  stands  in  its  way. 


RADIO   COMMUNICATION. 


237 


A  receiving  antenna  needs  to  be  large,  in  order  to  gather  in  enough 
energy  from  the  electric  waves  to  affect  the  receiving  apparatus. 
Likewise  a  sending  antenna  needs  to  have  large  dimensions,  in  order 
to  send  electric  waves  to  a  greater  distance.  The  same  antenna  is 
often  used  for  both  sending  and  receiving.  An  antenna  used  for 


receiving  only  may,  however,  be  made  simpler  than  one  which  is 
also  required  for  sending  purposes. 

The  simplest  form  of  antenna  would  be  a  plate  P,  Fg.  163,  sup- 
ported  above  the  earth  and  insulated  from  it,  except  for  the  connec- 


238  RADIO   COMMUNICATION. 

tion  through  the  wire  W,  called  the ' '  lead-in  wire  "  or ' '  lead-in.  "  The 
plate  and  the  earth  form  the  two  terminals  of  a  condenser,  the  space 
between  them  furnishing  the  dielectric.  When  an  alternating  emf. 
is  introduced  into  the  wire,  charging  currents  flow  into  and  out  of  P 
and  the  earth,  the  dielectric  being  strained  first  in  one  direction  and 
then  in  the  other.  As  has  been  explained  in  the  previous  chapter, 
these  strains  are  equivalent  to  displacement  currents  of  electricity 
through  the  dielectric,  which  serves  to  complete  the  circuit.  A  region 
in  which  the  dielectric  is  undergoing  alternating  strains  is  the  start- 
ing point  of  electric  waves.  The  larger  the  plate  and  the  higher  it 
is  raised  from  the  earth,  the  greater  the  amount  of  space  in  which 
this  strained  condition  exists,  and  the  more  powerful  the  waves 
which  are  radiated. 

In  practice,  wires  are  used  for  an  antenna  instead  of  plates.  A 
single  vertical  wire  is,  for  its  size,  the  best  radiator,  but  it  has  to  be 
made  extremely  long  in  order  to  get  sufficient  capacitance  for  long 
wave  or  long  distance  work  (Section  142").  Antennae  of  different 
numbers  of  horizontal  or  inclined  wires  instead  are,  however, 
practicable  and  radiate  very  well.  It  must  be  thoroughly  under- 
stood that  an  antenna  is  merely  a  large  condenser  and  may  have 
various  shapes  consistent  with  this  condition,  although  some  forms 
will  radiate  electric  waves  much  better  than  others. 

138.  Different  Types.1— The  umbrella  type  of  antenna,  Fig.  164, 
consists  of  a  number  of  wires  which  diverge  from  the  top  of  a  mast, 
and  are  attached  to  anchors  in  the  ground  through  insulators,  A,  as 
shown  in  the  figure.  Lead-in  wires  L  are  brought  down  from  the 
junction  of  the  wires  B  to  the  apparatus.  The  portions  of  wire  BA 
take  the  place  of  the  plate  P  of  Fig.  163.  This  antenna  may  be 
erected  quickly,  and  is  used  for  radio  pack  sets. 

An  antenna  of  horizontal  parallel  wires,  supported  between  two 
masts  and  insulated  therefrom,  is  common.  This  is  the  standard 
form  for  ship  stations.  According  as  the  lead-in  wires  are  attached 
at  the  end  of  the  horizontal  wires  (Fig.  165)  or  at  their  center  (Fig.  166) 
the  antenna  is  said  to  be  of  the  inverted  L  or  of  the  T  type.  The  V 
antenna  consists  of  two  sets  of  horizontal  or  slightly  inclined  wires, 
supported  by  three  masts,  so  that  the  horizontal  portions  form  an 
angle,  Fig.  167. 

For  short  distance  sending,  simpler  antennae  may  be  used,  such 
as,  for  example,  a  simple  wire  supported  between  two  stakes  at  a 
height  of  only  a  few  feet  from  the  ground.  For  emergencies,  a  long 
i  See  also  S.  C.  Radio  Pamphlet  No.  2. 


RADIO   COMMUNICATION. 


239 


insulated  wire  may  be  laid  upon  dry  ground,  the  apparatus  being 
inserted  at  the  middle,  forming  what  is  known  as  a  "ground  an- 
tenna." For  receiving  stations  equipped  with  amplifiers  or  other 
delicate  receiving  apparatus,  very  simple  antennae  may  be  employed, 
even  for  long-distance  work. 

139.  Current  and  Voltage  Distribution  in  an  Antenna. — "When  an 
emf.  is  introduced  into  an  antenna,  a  charging  current  flows  in  the 
wires  as  was  described  in  the  ideal  case  of  Fig.  163.  If  we  attempt 
to  form  a  picture  of  this  process  in  the  wire  antenna,  we  must  remem- 
ber that  every  inch  of  the  wire  forms  a  little  condenser,  with  the  earth 
acting  as  the  other  plate.  The  antenna  is  said  to  have  a  distributed 
capacitance. 

As  the  electricity  flows  from  the  bottom  of  the  antenna,  some  of  it 
accumulates  on  each  portion  A  of  the  wire,  causing  a  displacement 


Displacement    currants 
from  an  antenna 


Distribution  of  current 
and  voltage  alon^an 
antenna 


.Ho   Analogy  of/ 

,*\  klo  motion, lar^je. force 
c;         ',  Large  motion,  small  force 

^  Uo  motion ,  lar^,e  force 

Current  Klo  eUrrent 

lari«  volt^e 

Larke.  corner 
Ho  Voltage 


current  through  the  dielectric  to  earth,  as  shown  in  AB  (Fig.  168). 
The  current  in  the  wire  accordingly  diminishes  as  the  free  end  F  of 
the  antenna  is  approached,  and  becomes  zero  at  that  "end.  The  cur- 
rent is  evidently  different  at  different  parts  of  the  antenna,  being 
zero  at  the  free  end  and  a  maximum  where  the  antenna  is  connected 
to  the  ground  (Fig.  169).  This  is  in  marked  contrast  to  the  case  of  a 
direct  current,  which  always  has  the  same  value  at  every  point  of  the 
circuit.  The  difference  here  is  brought  about  by  the  very  high 
frequency  of  the  currents. 

The  voltage  of  the  antenna,  on  the  contrary,  is  zero  at  the  grounded 
end  and  has  a  maximum  value  at  the  free  end.  In  fact,  the  latter  is 
the  point  where  the  most  intense  sparks  can  be  drawn  off;  therefore 
the  insulation  of  the  antenna  from  nearby  objects  and  the  earth  must 
be  particularly  good  at  this  point.  (In  Fig.  169  the  voltage  and  cur- 


240  RADIO   COMMUNICATION. 

rent  are  supposed  to  be  measured  by  the  horizontal  distance  from  the 
solid  vertical  line.) 

A  large  capacitance  to  earth,  concentrated  at  any  point  of  the 
antenna,  causes  a  large  change  in  the  current  at  that  part  of  the  an- 
tenna. If  this  bunched  capacitance  is  located  at  the  top  of  the 
antenna,  such  as  is  the  case  with  a  flat  topped  antenna  of  long  wires, 
with  only  a  few  vertical  lead-in  wires,  the  average  current  in  the 
flat  top  portion  will  be  large,  and  it  increases  slightly  in  strength  as 
the  charges  pass  down  through  the  lead-in  wire  (picking  up  the 
charges  there),  hence  giving  a  large  current  through  the  receiving 
apparatus.  It  is  a  distinct  advantage  to  have  as  large  a  part  of  the 
total  capacitance  of  the  antenna  as  possible  at  the  top. 

140.  Action  of  the  Ground.  Counterpoises. — The  electric  oscilla- 
tions in  an  antenna  may  be  regarded  as  somewhat  analogous  to  the 
vibrations  of  a  string,  stretched  between  two  points  A  and  B,  and 
plucked  at  the  middle,  C,  in  Fig.  170.  The  stretching  forces  on  the 
string  are  greatest  at  the  points  A  and  B,  while  the  portion  C  is  under 
very  small  force.  The  motion  of  the  string  is  most  considerable  at  C, 
while  the  points  A  and  B  do  not  move.  If  we  regard  current  as 
similar  to  motion  and  voltage  to  force,  we  can  see  (according  to  state- 
ment in  the  preceding  section)  that  the  top  of  the  antenna  resembles 
in  its  behavior  the  end  A  (or  B)  of  the  string,  while  the  bottom  of  the 
antenna  corresponds  to  the  point  C  of  the  string. 

The  part  played  by  the  earth  may  now  be  understood.  If  we 
suppose  for  a  moment  that  the  antenna  is  disconnected  from  the 
ground  and  insulated,  then  the  lower  free  end  would  become  a  point 
where  the  current  would  be  zero  and  where  the  variations  of  voltage 
would  be  large  (corresponding  to  point  J5,  Fig.  170).  The  portion 
where  the  current  would  be  a  maximum  would  lie  at  some  elevated 
point.  To  set  a  string  in  vibration  requires  the  smallest  force  when 
it  is  plucked  at  the  middle.  Right  at  the  ends  it  is  almost  impossible 
to  set  it  in  vibration.  Just  so,  the  antenna,  if  disconnected  from 
earth,  would  be  almost  impossible  to  set  in  vibration  if  the  emf .  were 
applied  at  the  bottom  end.  For  successful  working,  the  exciting 
apparatus  would  have  to  be  joined  to  inaccessible  points  of  the  wire 
higher  up.  It  is  necessary,  then,  to  make  sure  that  the  lower  end  of 
the  antenna  is  a  region  where  a  current  is  large,  and  with  a  good 
ground  this  condition  is  satisfied. 

In  places  where  the  ground  has  poor  conductivity  (dry,  rocky 
soil,  with  ground  water  at  some  considerable  depth)  it  becomes  diffi- 
cult to  satisfy  the  above  condition.  In  such  cases  an  earth  capaci- 


RADIO  COMMUNICATION. 


241 


tance  or  ' '  counterpoise  "  must  be  used.  This  is  merely  an  insulated 
mass  of  metal  M  of  large  extent  (Fig.  171)  placed  near  the  ground. 
The  lower  end  of  the  antenna  is  joined  to  the  metal  which  forms  the 
upper  plate  of  a  condenser,  while  the  more  moist  layers  W  of  the 
earth,  deep  below  the  surface,  form  the  lower  plate.  As  far  as  the 
antenna  is  concerned,  the  counterpoise  takes  the  place  of  the  ground. 
The  antenna  can,  therefore,  be  excited  by  suitable  apparatus  placed 
in  the  antenna,  or  coupled  to  it  just  above  M  or  near  the  ground. 
(The  connecting  of  the  generating  apparatus  to  the  antenna  is 
treated  in  Sec.  160.)  'In  some  cases,  a  netting  of  wires  placed  near 
the  earth  is  used  as  a  counterpoise,  in  others,  insulated  wires  are  car- 
ried from  the  base  of  the  antenna  and  laid  out  upon  the  ground. 

In  airplane  radio  outfits  a  counterpoise  must  necessarily  be  used. 
This  is  furnished  by  the  metal  wires  of  the  framework,  the  engine, 


F 

IMHH 

aim 

Pi  a  n^                p| 

\     \          xx               x^^            *iorth 
\    /                 «               X  /' 

5.  113 

v 

I 

.:.-/..  w  '•'.'•-  :  •'.  -  '  ' 

Variation   of  the                     llluaTratinft  Method 
LffeotiVe    S^esiaTdnce          o^  tn'Ar^ulatt'en 
sfan   Antenna 

C  o  u  nter  JSP  !  5e 

stay  wires,  metallized  wings,  etc.  The  antenna  proper  consists  of  a 
weighted  wire  let  down  from  the  airplane,  which  trails  behind  when 
in  flight.  A  reel  allows  this  to  be  coiled  up  when  a  landing  is  to 
be  made.  On  airplanes  the  antenna  is  below  the  counterpoise,  but 
the  action  is  not  different  from  the  ordinary  antenna  and  counter- 
poise systems. 

F.  Antenna  Characteristics. 

The  behavior  of  an  antenna  depends  upon  its  capacitance,  in- 
ductance, and  effective  resistance  just  as  is  the  case  with  any  oscil- 
lating circuit.  The  capacitance  and  inductance  determine  the 
length  of  the  radiated  waves  (see  Sec.  116);  the  resistance  determines 
the  damping. 

97340° — 19 16 


242  RADIO  COMMUNICATION. 

141.  Capacitance.  —  The  energy  which  can  be  given  to  a  con- 
denser, when  it  is  charged  to  a  voltage  E,  is  equal  to  one-half  the 
capacitance,  C,  multiplied  by  the  square  of  the  voltage.  The 
energy  which  is  supplied  to  an  antenna  each  second  when  it  receives 
N  charges  per  second  is,  therefore  (as  given  in  Sec.  34), 


We  may,  evidently,  increase  the  supply  of  power  to  an  antenna  by 
increasing  the  number  of  charges  per  second,  or  by  raising  the  voltage. 

It  is  not  practicable  to  raise  the  rate  of  charging  beyond  about 
1000  to  1500  sparks  per  second.  The  voltage  on  the  antenna  can- 
not be  made  greater  than  about  50,000  volts  without  loss  of  power 
through  leakage  and  brush  discharges.  The  only  remaining  factor 
which  can  be  varied  is  C  in  the  above  formula;  therefore,  a  high 
power  sending  antenna  must  have  a  large  capacitance.  Large 
capacitance  means  many  wires  of  great  length;  that  is,  a  large  and 
costly  structure. 

The  capacitance  of  a  single  wire  parallel  to  the  ground  can  be  cal- 
culated approximately,  as  also  the  capacitance  of  certain  simple 
arrangements  of  parallel  wires  (see  C.  74,  pp.  237-242).  Even  in  the 
simplest  cases,  however,  the  presence  of  houses,  trees  and  other 
neighboring  objects,  and  the  difficulty  of  allowing  for  the  lead-in 
wire,  makes  any  precise  calculation  impossible.  It  should  be  noted, 
however,  that  the  capacitance  of  a  wire  is  proportional  to  its  length. 
The  capacitance  of  two  wires  near  together  is  less  than  the  sum  of 
their  capacitances,  and,  in  general,  although  each  added  wire  adds 
something  to  the  capacitance,  it  adds  much  less  than  the  capacitance 
it  would  have  alone  in  the  same  position.  As  an  indication  of  what 
values  of  antenna  capacitance  may  be  expected,  the  following  values 
may  be  cited  : 

Airplane  and  small  amateur  antennae,  about  0.0005  mfd. 

Ship  antennae,  0.0007  to  0.0015  mfd. 

Large  land  station  antennae,  0.005  to  0.015  mfd. 

That  is,  in  spite  of  their  size  and  extent,  antennae  do  not  possess 
greater  capacitance  than  is  found  in  ordinary  variable  air  condensers 
(see  Sec.  .32). 

The  capacitance  of  an  antenna  is  easily  measured  by  a  substitu- 
tion method  (L.  W.  Austin).  The  wire  from  the  antenna  and  that 
from  the  ground  are  connected  to  an  inductance  coil  of  such  value 
as  to  give  a  wave  length  five  or  more  times  the  fundamental  (Sec. 


RADIO   COMMUNICATION.  243 

144).  A  generating  circuit  is  loosely  coupled  to  this  and  varied  to 
resonance.  The  connections  to  antenna  and  ground  are  then  re- 
moved from  the  inductance  coil  and  replaced  by  a  variable  con- 
denser, which  is  then  varied  to  resonance.  The  condenser  setting 
gives  the  antenna  capacitance.  This  is  subject  to  a  small  correc- 
tion for  the  antenna  inductance,  which,  however,  may  usually  be 
neglected. 

142.  Inductance. — Although  principal  stress  has  been  laid  upon 
the  conception  of  the  antenna  as  a  condenser,  the  inductance  which 
its  wires  necessarily  possess  is  of  equal  importance  in  determining 
the  wave  length  of  the  radiated  waves.     The  antenna  is,  in  fact,  an 
oscillating  circuit,  and  as  such  the  wave  length  or  frequency  of  free 
oscillation  depends  upon  the  product  of  the  inductance  and  capaci- 
tance.    See  formula  (79),  Section  116. 

The  inductance  in  general  is  not  large — 50  to  100  microhenries  is 
a  common  range  of  values — but  larger  capacitance  is  necessarily 
associated  with  larger  inductance,  so  that  high-power  antennae  are 
naturally  long  wave  antennae.  Methods  for  measuring  inductance 
and  capacitance  of  antennae  are  described  in  C.  74,  pp.  79,  83  to 
86,  and  98.  Antenna  inductance  is  more  commonly  obtained  from 
a  combination  of  measurements  of  capacitance  and  wave  length. 

143.  Resistance. — The  wires  of  an  antenna  offer  resistance  to  the 
current,  which  is  greater  for  the  high  frequency  antenna  current 
than  it  would  be  for  a  steady  current,  on  account  of  the  skin  effect 
(see  Sec.  117).     In  addition  to  this,  the  radiation  of  energy  in  waves 
causes  a  further  increase  in  the  apparent  resistance  of  the  antenna. 
The  ''effective  resistance  of  the  antenna"  is  denned  as  the  quotient 
of  the  power  given  to  the  antenna  by  the  square  of  the  antenna  cur- 
rent.   That  is,  if  R  is  the  effective  resistance,  the  total  power  put 
into  the  antenna  is  RP,  where  /  is  measured  at  the  base  of  the 
antenna.     The  effective  resistance  is  different  for  different  fre- 
quencies, as  is  shown  below. 

The  total  power  is  dissipated  in  the  following  ways,  (1)  as  heat  in 
the  antenna  wires  and  earth  connection,  (2)  brush  discharge,  (3) 
leakage  over  or  through  insulators,  (4)  heat  in  the  dielectric  Bur- 
rounding  the  antenna,  and  in  any  condensers  that  are  in  the  antenna 
circuit,  and  (5)  radiated  waves.  Part  of  (5)  will  also  be  turned  into 
useless  heat  by  inducing  eddy  currents  in  near-by  conductors,  such 
as  guy  wires  or  metal  masts.  If  Tt"/2  represents  all  the  power  except 
that  radiated,  and  R"I2  represents  the  power  radiated  as  waves, 


244  RADIO   COMMUNICATION. 

then  it  is  evident  that  RT-+R//I2=R  I2,  or  R'+R"=R,  the  effec- 
tive resistance.  R"  is  called  the  "radiation  resistance."  It  might 
bo  denned  as  that  resistance  which,  if  placed  at  the  base  of  the 
antenna,  would  cause  as  great  a  dissipation  of  energy  as  the  energy 
radiated  in  waves.  It  will  be  different  at  different  frequencies. 
It  gives  an  idea  of  the  radiating  power  of  the  antenna  for  each 
ampere  of  antenna  current. 

When  the  effective  resistance  of  an  antenna  is  measured  at  a 
number  of  frequencies  and  the  results  are  plotted,  a  curve  is  ob- 
tained like  curve  4,  Fig.  172.  The  shape  of  the  curve  is  explained 
by  considering  the  laws  according  to  which  the  different  kinds  of 
resistance  in  the  antenna  vary  with  the  wave  length.  The  radia- 
tion resistance  decreases  as  the  square  of  the  wave  length  increases. 
Such  a  variation  is  represented  by  curve  1,  Fig.  172.  The  resist- 
ance of  the  conductors  and  earth  connection  is  nearly  constant  with 
different  wave  lengths,  curve  2.  The  dielectric  resistance  increases 
nearly  as  the  wave  length,  curve  3.  Curve  4  is  the  sum  of  curves 
1,  2,  3.  If  the  losses  in  the  dielectric  are  very  small  the  curve  does 
not  have  a  minimum,  as  at  A,  but  becomes  horizontal  at  the  right 
end.  If  these  are  negligible,  the  curve  merely  falls  toward  a  lim- 
iting value. 

To  reduce  the  dielectric  losses  no  portion  of  the  antenna  should 
be  in  contact  with  buildings  or  trees.  To  reduce  eddy  current 
losses  care  should  be  taken  to  have  the  antenna  a  reasonable  distance 
from  guy  wires,  and  especially  large  masses  of  metal.  Guy  wires 
may  be  cut  up  and  insulated  in  sections.  On  shipboard,  induced 
currents  are  produced  in  iron  stacks  and  guy  wires  near  the  antenna, 
and  in  cases  where  the  frequency  of  the  waves  agree  with  the  natural 
frequency  of  oscillation  of  these  metal  objects,  considerable  power 
losses  may  result.  These  show  themselves,  when  they  are  present, 
as  humps  on  the  experimental  curve  4,  Fig.  172,  at  the  frequencies 
in  question. 

The  effective  resistance  of  an  antenna  is  often  as  high  as  20  to  30 
ohms  at  the  fundamental  wave  length.  The  minimum  value  may 
be  5  to  10  ohms  for  a  land  station  and  as  low  as  2  ohms  for  a  ship 
station. 

144.  Wave  Length,  and  Its  Measurement.— The  wave  length  of 
the  waves  emitted  by  an  antenna,  when  no  added  inductance  or 
capacitance  is  inserted  in  the  antenna  circuit,  is  known  as  its  "funda- 
mental wave  length."  By  putting  inductance  coils  ("loading  coils  ") 
in  the  antenna  circuit,  longer  v;aves  may  l:e  radiated,  while  on  the 


RADIO   COMMUNICATION.  245 

contrary,  capacitances  put  in  series  with  the  antenna  enables  it  to 
produce  shorter  waves  than  the  fundamental.  The  use  of  a  series 
condenser  is  avoided  where  possible,  since  it  has  the  effect  of  decreas- 
ing the  total  capacitance  of  the  antenna  circuit  (Capacitances  in 
Series,  Sec.  35)  and  thereby  diminishing  the  amount  of  power  which 
can  be  given  to  the  antenna.  The  addition  of  some  inductance  has 
a  beneficial  effect,  since  the  decrement  of  the  antenna  is  thereby 
lessened  and  a  sharper  wave  results.  It  is  not  advisable  to  load  the 
antenna  with  a  very  great  inductance,  however,  as  it  is  not  an  effi- 
cient radiator  of  waves.  The  waves  emitted  are  very  much  longer 
than  the  fundamental  wave  length.  As  a  general  rule,  small  send- 
ing stations,  for  short  ranges,  work  best  on  short  waves,  and  long- 
distance stations  on  long  waves.  Long  waves  have  the  advantage 
for  long-distance  work  that  they  are  not  absorbed  in  traveling  long 
distances  to  the  extent  that  short  waves  are. 

The  United  States  radio  laws  specify  that  high-power  stations  shall 
use  waves  longer  than  1600  meters,  that  the  Navy  has  the  range 
from  1600  to  600  meters,  that  ship  stations  shall  transmit  on  a  wave 
length  of  300,  450,  or  600  meters,  while  amateurs,  when  permitted  to 
work,  must  confine  themselves  to  waves  shorter  than  200  meters. 
The  majority  of  high  power  stations  use  waves  longer  than  3000 
meters,  and  10,000  to  15,000  meters  are  used  by  some.1 

Measurement  of  Antenna  Wave  Length. — For  a  simple  vertical  wire 
grounded  antenna  the  fundamental  wave  length  is  slightly  greater 
than  four  times  the  length  of  the  wire.  The  constant  is  often  used 
as  4.2,  and  applies  approximately  also  to  flat  top  antennas  (L  or  T 
types)  with  vertical  lead-in  wire,  the  total  length  being  measured 
from  the  transmitting  apparatus  up  the  lead-in  wire  and  over  to  the 
end  of  the  flat  top.  It  is  usually  easier,  and  certainly  more  accurate, 
to  measure  the  wave  length  radiated  from  an  antenna  directly  by 
the  use  of  a  wavemeter.  (Sec.  112.)  The  wavemeter  coil  needs 
merely  to  be  brought  somewhere  near  the  antenna  or  lead-in  wire 
and  the  condenser  of  the  wavemeter  adjusted  to  give  maximum  cur- 
rent in  the  wavemeter  indicator.  The  wave  length  corresponding 
to  the  wavemeter  setting  is  then  the  length  of  the  waves  radiated 

i  It  appears  likely  that  in  the  future  the  legally  prescribed  values  will  be  changed. 
Possibly  the  range  of  from  200  to  2000  meters  will  be  reserved  for  land  stations, 
except  for  a  small  range  around  COO  meters  for  airplanes,  while  ship  stations  will  be 
required  to  use  2000  to  6000  meters,  and  above  this  limit  high  power  stations  will 
work. 


246  RADIO    COMMUNICATION. 

"by  the  antenna.  If  the  loading  coil  and  series  condenser  are  cut 
out,  the  measured  wave  length  is  the  "fundamental  wave  length" 
of  the  antenna. 

145.  Harmonics  of  Wave  Length. — A  simple  radio  circuit  has  a 
reactance  equal  to  zero  at  a  single  frequency,  namely,  the  resonance 
frequency,  and  the  maximum  current  possible  with  the  given  emf. 
will  then  flow.     This  result  is  strictly  true  only  when  the  capaci- 
tance and  inductance  are  concentrated  at  definite  points  of  the  cir- 
cuit.    In  an  antenna,  however,  the  inductance  and  capacitance  are 
•distributed,  and  it  is  found  that  a  maximum  of  current  is  obtained 
ior  a  whole  series  of  different  frequencies  or  wave  lengths. 

What  is  called  the  " fundamental  frequency"  is  the  lowest  fre- 
quency for  which  the  current  attains  a  maximum,  when  not  loaded 
"with  either  capacitance  or  inductance.  Denoting  this  by/,  there 
are  in  the  same  antenna  other  resonance  frequencies  3/,  5/,  7f,  etc., 
called  the  ''harmonic  frequencies"  of  the  antenna.  With  the  usual 
methods  of  producing  current  in  an  antenna  it  radiates  principally 
waves  of  its  fundamental  frequency  alone;  free  oscillations  of  the 
harmonic  wave  lengths  are  almost  entirely  lacking.  However,  when 
^mfs.  having  the  harmonic  frequencies  are  applied,  vigorous  oscil- 
lations of  those  frequencies  may  be  set  up. 

146.  Directional   Effect. — It  is   desirable,    for   certain   purposes, 
that  the  energy  of  a  transmitting  antenna  may  be  sent  in  a  particular 
•direction.     The  range  of  a  station  may  thus  be  increased  and  inter- 
ference decreased.     Still  more  important  is  the  ability  of  an  antenna 
to  receive  waves  coming  from  a  single  direction,  but  to   offer  no 
response  to  waves  from  other  directions.     This  is  valuable  as  an 
•effective  means  of  reducing  interference,  since  in  general  the  inter- 
fering station  is  not  likely  to  lie  in  the  same  direction  as  that  with 
which  it  is  desired  to  communicate. 

A  further  and  very  important  application  of  antennae  with  direc- 
tional characteristics  is  the  possibility  of  triangulation.  If  C,  Fi%. 
173,  is  a  transmitting  station,  and  the  waves  come  in  to  station  A 
from  a  direction  which  makes  an  angle  x  with  the  north,  while  at 
station  B  waves  from  C  arrive  from  the  direction  BC,  which  makes 
an  angle  y  with  the  north,  then  the  positions  of  the  stations  A,  B,  C 
•can  be  calculated,  provided  only  that  the  distance  AB  and  the 
angles  x  and  y  are  known.  If  C  is  an  enemy  station,  it  may  be  lo- 
cated by  measurements  of  its  direction,  as  observed  from  receiving 
stations  A  and  B  whose  positions  are  known.  Or,  if  C  is  supposed 


RADIO    COMMUNICATION.  247 

to  be  a  lighthouse  station,  which  is  radiating  signals,  a  vessel  can 
determine  its  unknown  position  A,  even  in  a  fog,  by  observing  the 
direction  of  C,  and  then  after  sailing  a  known  distance  AB,  making 
similar  radio  observations  of  the  direction  of  C  from  its  new  position 
B.  The  positions  A  and  B  and  the  ship's  course  can  be  worked  out. 
Even  in  clear  weather  it  is  often  desirable  to  have  a  means  of  check- 
ing up  astronomical  observations  of  the  ship's  position,  since  a  small 
error  of  observation  may  have  serious  consequences  when  a  vessel 
is  near  the  coast. 

All  forms  of  unsymmetrical  antennae,  such  as  the  inverted  L  and 
the  V,  are  somewhat  directional  in  their  characteristics,  at  least  on 
land.  The  so-called  ground  antennae  give  considerably  better  trans- 
mission along  their  length  than  at  right  angles.  Closed  coil  aerials 
have,  however,  shown  themselves  particularly  adapted  to  this  hind 
of  work.  Further  details  are  given  in  Sections  151,  152  below. 

G.  Antenna  Construction. 

147.  Towers   and    Supports. — For   land    stations   wooden   masts 
have  been  much  employed.     For  portable  antennae  these  are  made 
in  sections  which  fit  together  like  a  fishing  rod.     For  higher  power 
stations,  latticed  metal  masts  are  common,  and  in  some  cases,  tubular 
metal  masts  in  telescoping  sections.     Except  in  special  instances, 
guy  ropes  or  wires  are  necessary,  and  in  some  cases  the  support  is 
sustained  entirely  by  these.     It  has  been  quite  generally  regarded 
as  a  structural  advantage  to  allow  a  small  freedom  of  movement  to 
the  mast,  so  that  it  may  rock  slightly  in  the  wind.    A  simple  one- 
wire  antenna  may  be  held  by  any  support  that  is  available.     When 
a  tree  is  used  to  support  either  end,  a  rope  should  run  out  for  some 
distance  from  the  tree,  and  the  wire  be  attached  to  this  by  an  insu- 
lator, so  that  the  antenna  wire  itself  may  not  be  in  or  near  the  tree. 
The  standard  flat  top  ship  antenna  makes  use  of  the  ship's  masts  for 
supports.     The  antenna  wires  are  stretched  between  two  booms  or 
spreaders  from  which  halyards  run  to  the  masts. 

148.  Insulators. — The  insulation  of  an  antenna  is  a  matter  re- 
quiring careful  attention.     The  system  depicted  in  Fig.  174  is  typ- 
ical of  a  ship's  antenna.     In  the  case  of  the  antennae  for  large  land 
stations,  the  guy  ropes  are  interrupted  by  insulators.     Porcelain, 
hard  rubber,  or  electrose  rods  into  which  eyebolts  are  molded  are 
common.     A  form  of  nearly  spherical  porcelain  insulator,  so  grooved 
as  to  carry  the  two  wires  firmly  without  their  coming  in  contact,  is 


248 


RADIO    COMMUNICATION. 


shown  in  Fig.  175.     In  the  event  of  this  insulator   breaking,  the 
wires  do  not  part. 

Where  the  lead-in  wires  from  the  antenna  pass  through  the  walls 
of  the  house  in  which  the  sending  and  receiving  apparatus  is  in- 
stalled, special  care  needs  to  be  taken  to  ensure  good  insulation.  A 
form  much  used  for  this  purpose  is  shown  in  Fig.  176.  In  the  case 
of  some  large  aerials,  the  supporting  mast  itself  has  to  be  insulated 


FlQ. 


Mast 


Mast 


ic&: 

Insulator  -for 
Le&d  -ir\  Wire  5 

i  WAII 


from  the  ground  at  its  base.  The  design  of  an  insulator  which  com- 
bines sufficient  mechanical  strength  with  good  dielectric  properties 
is  a  difficult  matter. 

149.  Antenna  Switch.  Conductors. — An  antenna  switch  is  a  ne- 
cessity in  all  permanent  installations.  This  has  the  function  of  dis- 
connecting the  receiving  apparatus  from  the  antenna  completely, 


RADIO    COMMUNICATION,  249 

when  a  message  is  to  be  sent,  and  vice  versa.  The  action  of  such  a 
switch  is  made  such  that  it  is  impossible  for  the  operator  to  make  a 
mistake  and  impress  the  large  sending  voltage  upon  the  delicate  re- 
ceiving apparatus.  Since  the  currents  in  the  antenna  wires  have  a 
high  frequency,  the  resistance  at  radio  frequencies  is  larger  than  at 
ordinary  low  frequencies.  (See  Sec.  117.)  Phosphor  bronze  wires 
of  seven  or  more  strands  are  commonly  used. 

150.  Grounds  and  Counterpoises. — To  obtain  a  good  conducting 
ground  connection  is  a  comparatively  easy  matter  in  a  ship  station. 
In  a  steel  ship,  a  wire  is  merely  attached  to  the  hull  of  the  ship  and 
the  good  conductivity  of  the  sea  water  assures  an  intimate  connec- 
tion with  the  ground.  On  a  wooden  ship,  a  large  plate  of  metal  is 
attached  to  the  outside  of  the  hull,  under  water,  and  the  ground 
wire  is  connected  to  it. 

The  ground  connections  of  some  land  stations  are  often  very  elab- 
orate, a  considerable  number  of  copper  plates  or  heavy  wires,  ar- 
ranged radially  from  the  foot  of  the  antenna,  being  buried  in  moist 
earth.  In  general,  the  endeavor  is  made  to  insure  a  considerable 
area  of  conducting  material  in  contact  with  the  moist  earth.  Coun- 
terpoises are  especially  useful  when  the  soil  is  dry  and  rocky,  or 
when  time  is  not  available  for  making  a  ground  connection.  The 
counterpoise  may  consist  of  a  considerable  area  of  wire  netting,  sup- 
ported parallel  to  the  ground,  or  laid  upon  it;  or  insulated  wires  may 
be  carried  radially  from  the  foot  of  the  antenna,  being  held  at  a  short 
distance  from  the  ground.  The  amount  of  wire  used  in  the  counter- 
poise should  be  as  much  as,  or  more  than,  that  used  in  the  antenna 
proper.  The  antenna  should  always  be  grounded  through  a  special 
switch,  when  not  in  use,  to  avoid  possible  damage  from  lightning. 

H.  Closed  Coil  Aerials. 

Although  closed  circuits  are  by  no  means  as  powerful  radiators  or 
receivers  of  electric  waves  as  the  usual  forms  of  antenna,  they  possess 
strong  directional  characteristics,  and  are  used  in  installations  where 
this  property  is  especially  desired.  An  inverted  L  antenna  is  very 
common  when  it  is  desired  to  transmit  in  a  single  chosen  direction, 
but  for  directional  receiving,  the  closed  coil  is  universally  used. 
The  relative  strength  of  signal  obtainable  with  antennae  and  closed 
coils  may  be  calculated  from  the  transmission  formulae  given  in 
Section  134. 


250  RADIO    COMMUNICATION. 

The  problem  of  confining  the  radiated  waves  to  a  limited  range 
of  directions  has  not,  however,  been  very  satisfactorily  solved. 
There  is  a  marked  tendency  for  the  wave  front  to  become  spherical 
as  the  wave  travels  forward,  and  thus  lose  the  form  it  had  in  the 
vicinity  of  the  radiator. 

A  much  more  important  consideration  is  the  location  of  the 
direction  from  which  waves  come  to  the  receiving  station,  and  for 
this  the  action  of  an  aerial  consisting  of  a  Hat  coil  of  few  turns  is  very 
successful. 

151.  Directional  Curve. — Fig.  177  gives  a  graphical  idea  of  the 
variation  of  the  received  current  in  the  coil  when  its  plane  is  revolved 
so  as  to  make  different  angles  with  the  direction  of  the  incoming 
waves.  In  the  figure,  the  direction  of  the  incoming  waves  is  along 
the  line  AB.  If  0 A  represents  the  received  current  when  the  plane 
of  the  coil  is  along  this  direction,  then  the  effect  of  rotating  the  coil, 
so  that  its  plane  stands  in  the  direction  MN.  is  to  reduce  the  received 
current  from  OA  to  ON.  When  the  plane  of  the  coil  makes  a  right 
angle  with  the  direction  of  waves,  the  line  MN  would  become 
tangent  to  both  circles  and  the  distance  ON  would  become  zero. 
No  current  should  then  be  received  when  the  plane  of  the  coil  is  at 
right  angles  to  the  direction  of  the  incoming  waves.  From  the  sym- 
metry of  the  diagram,  it  is  clear,  however,  that  the  received  current 
should  be  the  same  for  two  positions  of  the  coil  at  180°  with  one 
another,  for  example,  OA  and  OB,  or  OJVand  OM.  Usually,  how- 
ever, there  are  other  considerations  that  enable  the  operator  to 
determine  in  which  of  the  two  possible  directions  the  transmitting 
station  lies. 

To  make  a  determination  of  direction,  the  closed  coil  aerial, 
standing  with  its  plane  vertical,  is  connected  to  a  variable  condenser 
to  form  a  closed  oscillating  circuit.  The  circuit  is  tuned  by  means 
of  the  condenser,  to  the  wave  length  of  the  incoming  wave.  A  suit- 
able detecting  circuit  is  connected  to  the  terminals  of  the  condenser. 
A  horizontal  graduated  circle  is  provided  to  identify  the  position 
of  the  plane  of  the  coil.  The  coil  is  then  rotated  on  its  vertical  axis, 
until  the  signals  disappear.  There  will  usually  be  a  certain  range 
of  angular  positions  of  the  coil  for  which  no  response  will  be  obtained 
in  the  detector.  This  is  easily  explained  by  Fig.  177.  If  the 
radius  of  the  circle,  drawn  with  0  as  a  center,  represents  the  smallest 
received  current  which  causes  a  noticeable  effect  in  the  detecting 


RADIO    COMMUNICATION. 


251 


circuit,  then  it  is  evident  that  for  positions  of  the  coil  lying  within 
the  angles  COD  and  EOF,  no  signal  can  be  received. 

To  determine  the  direction  of  the  waves,  the  positions  C  and  D 
are  noted  on  the  graduated  scale,  for  which  the  signals  just  disappear 
and  just  become  audible,  respectively,  and  then  the  coil  is  turned 
about  180°  and  the  two  similar  positions  E  and  F  are  sought.  By 
taking  the  average  of  the  circle  readings  at  C  and  D,  and  E  and  F, 
that  position  of  the  coil  may  be  determined  which  lies  at  right  angles 
with  the  desired  direction.  The  instrument  is  set  up  at  the  start, 
so  that  the  scale  reading  will  give  directly  the  direction  of  the  waves 
in  degrees  from  the  north  and  south  line. 

With  proper  design,  it  is  possible  to  determine  the  direction  of  a 
sending  station  to  within  1°  or  2°  of  the  correct  value.  To 
obtain  such  accuracy,  however,  one  must  be  careful  that  no  masses 


.  H6 


FIC3.H9 


Direeti'onal  c.harac.1en'.stic. 
of  closed  coil  aerial 


Flat  spiral  acrid) 


Hie— 

f>n'*m  aerial 


of  iron,  or  other  metal,  or  any  object  which  is  capable  of  distorting 
the  wave  front  lies  in  the  vicinity  of  the  coil.  Neglect  of  this  pre- 
caution may  give  rise  to  determinations  of  direction  which  may  be 
easily  as  much  as  15°  in  error,  and,  in  the  case  of  very  short  waves, 
even  worse.  Where  a  mass  of  metal  has  a  fixed  position  relative  to 
the  radio  apparatus,  for  instance  the  engine  in  an  airplane,  the  set 
may  be  so  calibrated  as  to  eliminate  the  error  which  the  engine 
would  otherwise  cause  in  the  direction  indicated. 

152.  Constants  of  Closed  Coil  Aerials.— It  is  found  that  the 
maximum  received  current  in  a  closed-coil  aerial  is  greater,  the 
larger  the  number  of  turns  of  wire  on  the  coil,  the  greater  the  area 
of  the  coil,  and  the  greater  its  inductance.  The  current  varies 
inversely  as  the  resistance  and  the  square  of  the  wave  length.  For- 


252  RADIO    COMMUNICATION. 

mulae  for  the  current  received  in  terms  of  current  in  the  distant 
transmitting  aerial  are  given  in  Section  134. 

It  would  seem  at  first  sight  that  the  increase  in  resistance,  due  to 
increasing  the  number  of  turns  and  their  area,  would  be  offset  by 
the  rapid  increase  of  the  inductance  with  the  number  of  turns  and 
the  area  of  the  coil.  The  resistance  to  high  frequency  currents  is, 
however,  dependent  on  the  wave  length  and  increases  rapidly  as 
the  latter  approaches  the  value  of  the  fundamental  wave  length  of 
the  coil.  The  fundamental  wave  length  of  a  coil  aerial  is  that  which 
is  radiated  by  the  coil  when  no  capacitance  is  present  in  the  circuit 
except  that  between  the  turns  of  the  coil  itself  (Sec.  114.)  Com- 
pare with  Sec.  145.  As  a  guiding  rule  it  may  be  stated  that  a  closed 
coil  aerial  should  not  be  used  to  receive  waves  which  are  shorter 
than  about  two  or  three  times  the  fundamental  wave  length.  That 
is,  to  receive  short  waves  a  coil  of  small  inductance  and  capacitance 
should  be  used.  Such  a  coil  must  have  few  turns.  To  receive 
longer  waves,  coils  of  a  larger  number  of  turns  may  be  used.  Experi- 
ence shows  that  best  results  are  obtained  with  one  or  two  turns 
embracing  a  large  area  for  use  with  short  waves,  and  for  long  waves, 
coils  with  20  to  30  turns,  not  so  large  in  area. 

For  convenience  of  construction,  square  coils  are  found  to  be  the 
most  suitable.  The  wire  may  be  wound  in  a  flat  spiral,  Fig.  178, 
or  on  the  surface  of  a  square  prism,  Fig.  179.  Flat  spirals  of  only 
a  few  turns  are  used,  since  the  inner  turns  rapidly  become  less 
useful  as  the  area  diminishes.  The  spacing  of  the  wires  is  determined 
by  the  allowable  capacitance  of  the  coil. 

The  capacitance  of  a  coil  of  given  dimensions  increases  with  the 
number  of  turns,  at  first  rapidly,  and  then  more  slowly.  With  the 
wires  close  together,  the  capacitance  is  a  maximum  and  grows 
rapidly  less  when  the  wires  are  separated,  until  a  certain  critical 
spacing  is  reached,  beyond  which  the  capacitance  changes  very 
slowly. 

For  a  square  coil  8  ft.  on  a  side,  the  wires  should  be  placed  at 
least  0.35  in.  apart;  for  one  4  ft.  square,  0.2  in.;  and  for  a  2  ft.  coil, 
i/g  in.  Increasing  the  distance  between  the  wires  decreases  the 
inductance  of  the  coil;  at  the  same  time  it  reduces  the  capacitance. 
However,  it  is  found  that,  for  a  given  length  of  wire,  properly  spaced 
as  just  indicated,  the  fundamental  wave  length  of  the  coil  is  about 
the  same  with  different  dimensions.  This  fact  is  illustrated  in  the 
following  table,  where  96  ft.  of  wire  are  used  in  each  case. 


RADIO    COMMUNICATION. 

Characteristics  of  Closed  Coil  Aerials. 


253 


Length 
of  a  side 
of  the 
scmare 
(feet;. 

Number 
of 
turns. 

Spacing 
of 
wires 
(inch). 

Inductance 
(microhenries). 

Capacitance 
(micro-mfd.) 

Funda- 
mental 
wave 
length 
(meters). 

8 

3 

J 

96 

75 

160 

6 

4 

1 

124 

66 

170 

4 

6 

1 

154 

55 

174 

3 

8 

1 

193 

49 

183 

These  coils  should  be  used  with  a  condenser  of  sufficient  capaci- 
tance to  bring  them  into  resonance  at  500  to  600  meters.  The  first 
coil  would  be  most  suitable  for  these  wave  lengths,  on  account  of 
its  small  high  frequency  resistance,  and  greater  effective  area. 

The  range  of  coil  stations  when  used  with  field  sending  sets  is, 
of  course,  short.  When  used  to  receive  powerful  stations,  however, 
surprisingly  good  results  have  been  obtained.  Thus  the  great 
European  transatlantic  stations  have  been  heard  in  Washington 
with  coil  aerials  such  as  have  been  described,  using  vacuum  tube 
amplifiers.  An  instance  is  on  record  where  all  the  great  European 
stations  were  received  in  France  by  a  coil  aerial  only  18  cm.  square, 
having  200  turns. 


CHAPTER  5. 

APPARATUS  FOR  TRANSMISSION  AND  RECEPTION 

(Exclusive  of  Vacuum  Tubes.) 

A.  Apparatus  for  Damped  Wave  Transmission. 

153.  Function  of  Transmitting  Apparatus. — Electric  waves,  by 
means  of  which  radio  communication  is  carried  on,  are  produced  by 
the  transmitting  apparatus.     Power  must  be  supplied  by  some  kind 
of  electric  generator;  this  must  be  converted  into  high  frequency 
currents  which  flow  in  the  transmitting  aerial  and  cause  electric 
waves  which  travel  out  through  space.     The  waves  may  be  un- 
damped or  damped.     Damped  waves  consist  of  groups  or  trains  of 
oscillations  repeated  at  regular  intervals,  the  amplitude  of  the  oscil- 
lations in  each  train  decreasing  continuously.    The  number  of  these 
trains  of  waves  per  second  is  some  audible  frequency.     When  such 
waves  strike  a  receiving  apparatus  (described  later),  they  cause  a 
tone  in  the  telephone  receiver.     Signals  are  produced  by  means  of 
a,  sending  key,  which  lets  the  trains  of  waves  go  on  for  a  short  length 
of  time  (producing  a  dot)  or  a  longer  time  (producing  a  dash). 

The  principles  of  damped  and  of  undamped  waves  are  the  same 
in  many  respects,  so  that  much  of  what  is  told  regarding  damped 
wave  apparatus  applies  to  undamped  waves  as  well.  Particular  at- 
tention is  first  given  to  damped  waves,  as  the  apparatus  is  simple 
and  easily  adjusted,  and  is  suitable  for  portable  sets  and  for  short- 
distance  communication. 

154.  Simple  Spark  Discharge  Apparatus. — Damped  oscillations  are 
produced  when  a  condenser  discharges  in  a  circuit  containing  induc- 
tance.   The  condenser  is  discharged  by  placing  it  in  series  with  a 
spark  gap  and  applying  a  voltage  to  it  high  enough  to  break  down  or 
spark  across  the  gap.     As  explained  in  Section  115,  the  oscillations 
produced  when  the  condenser  discharges  in  such  a  circuit  are 
damped  and  soon  die  out.    Methods  of  producing  a  regular  succes- 
sion of  such  condenser  discharges  are  explained  in  the  following.    A 
high  voltage  must  be  applied  to  the  condenser  at  regular  intervals. 
This  is  done  by  the  use  of  a  transformer.     Through  the  primary  of 
the  transformer  is  passed  either  an  alternating  current  or  a  current 

254 


RADIO    COMMUNICATION. 


255 


regularly  interrupted  by  a  vibrator  operated  by  the  transformer 
(induction  coil).  For  the  use  of  the  induction  coil,  as  in  radio 
trench  sets,  see  Section  157.  The  principle  is  best  studied  first  in 
the  alternating  current  method. 

In  Fig.  180,  P  and  8  are  the  primary  and  secondary  of  a  step-up 
transformer  (Section  58),  which  receives  power  from  an  a.c.  gener- 
ator. The  primary  may  be  wound  for  110  volts,  and  the  secondary 
for  5000  to  20,000  volts.  By  means  of  the  transformer  the  condenser 
C  is  charged  to  a  high  voltage,  and  stores  up  energy.  When  the 
voltage  becomes  great  enough  it  breaks  down  the  spark  gap  and  the 
discharge  takes  place  as  an  oscillatory  current  in  the  inductance 
coil  L  and  its  leads.  See  Section  115.  The  main  discharge  does  not 
take  place  through  the  turns  of  8  on  account  of  its  relatively  high 
impedance.  The  transformer  ia  sometimes  still  further  protected 


groove 

Fia  183 


Fiq    180 


Simple   •S(3arK  discharge 


from  the  condenser  discharge  by  inserting  choke  coils  (not  shown 
in  Fig.  180)  in  the  leads  between  the  transformer  and  condenser. 
These  obstruct  the  high  frequency  current,  but  do  not  hinder  the 
passage  of  the  low  frequency  charging  current  into  the  condenser. 
Fig.  181  shows  a  transformer  used  in  radio  sets. 

The  standard  generator  frequency  is  500  cycles  per  second.  This 
causes  the  condenser  to  discharge  1000  times  a  second,  once  for 
each  positive  and  negative  maximum  if  the  spark  gap  is  of  such 
length  as  to  break  down  at  the  maximum  voltage  given  by  the  trans- 
former. The  number  of  sparks  per  second  is  called  the  "spark 
frequency."  With  the  standard  spark  frequency  of  1000  per 
second  the  amount  of  power  the  set  sends  out  is  considerably  greater 


256 


RADIO   COMMUNICATION. 


than  it  would  be  at  a  low  frequency  like  60  cycles  per  second,  be- 
cause the  transmitted  radio  waves  are  more  nearly  continuous,  as 
will  be  shown  later.  The  radiated  wave  trains  strike  a  receiving 
antenna  more  frequently  and  their  amplitude  does  not  need  to  be  so 
great  to  produce  the  same  effect  as  stronger  waves  received  at  longer 
intervals  of  time.  The  higher  frequency  produces  a  tone  in  the 
receiving  telephone  that  is  more  easily  heard,  because  the  ear  is 
most  sensitive  to  sound  waves  of  about  1000  per  second  and  also 
the  tone  is  more  easily  heard  through  atmospheric  disturbances. 


FIG.  181.— Step-up  transformer  for  charging  condenser. 

A  60-cycle  supply  may  be  used  if  the  number  of  sparks  per  second  is 
increased  by  using  a  rotary  spark  gap  giving  several  sparks  per  cycle. 
See  Section  156. 

Each  condenser  discharge  produces  a  train  of  oscillations  in  the 
circuit,  and  each  train  of  oscillations  consists  of  alternations  of  cur- 
rent which  grow  less  and  less  in  amplitude.  This  is  illustrated  in 
Fig.  192,  and  the  comparative  lengths  of  the  trains  of  oscillations  and 
the  lapse  of  time  between  their  occurrence  are  discussed  in  Section 
160. 


RADIO    COMMUNICATION.  257 

155.  Transmitting  Condensers. — Before  discussing  the  means  of 
getting  the  oscillations  into  an  antenna  (Section  160),  the  appa- 
ratus used  in  generating  the  oscillations  will  be  described  in  detail. 

The  most  common  types  of  condensers  used  in  radio  transmitting 
circuits  use  mica  or  glass  as  the  dielectric,  with  tinfoil  or  thin  copper 
as  the  conducting  coatings.  Compressed  air  and  oil  condensers  are 
sometimes  used,  but  are  bulky.  For  very  high  voltages  the  con- 
denser plates  are  immersed  in  oil  to  prevent  brush  discharge.  For 
moderate  voltages  a  coating  of  paraffin  over  glass  jars,  especially  at 
the  edges  of  the  metal  foil,  will  satisfactorily  reduce  brush  discharge. 
For  calculation  of  the  size  of  transmitting  condenser  needed  see 
Section  170. 

156.  Spark  Gaps. — -When  the  gap  is  broken  down  by  the  high 
voltage  it  becomes  a  conductor,  and  readily  allows  the  oscillations 
of  the  condenser  discharge  to  pass.     During  the  interval  between 
discharges  the  gap  cools  off  and  quickly  (see  Section  160  and  Fig. 
193)  becomes  non-conducting  again.     If  the  gap  did  not  resume  its 
non-conducting  condition,  the  condenser  would  not  charge  again, 
since  it  would  be  short  circuited  by  the  gap,  and  further  oscillations 
could  not  be  produced.    The  restoration  of  the  non-conducting  state 
is  called    "quenching."     A   device   called   the    "quenched  gap" 
for  very  rapid  quenching  of  the  spark  is  described  below  in  this 
section.     Additional  appliances  for   the  prevention  of  arcing  are 
discussed  in  Section  167. 

Plain  Gap. — A  plain  spark  gap  usually  consists  of  two  metal  rods 
so  arranged  that  their  distance  apart  is  closely  adjustable.  See 
Fig.  182.  It  is  important  that  the  gap  be  kept  cool  or  it  will  arc; 
for  that  reason  the  sparking  surfaces  should  be  ample.  Often  the 
electrodes  have  fins  for  radiating  away  the  heat.  An  air  blast  across 
the  gap  will  greatly  aid  the  recharging  by  removing  the  ionized  air, 
to  which  the  conducting  power  of  the  gap  is  due.  At  the  sparking 
surfaces  an  oxide  slowly  forms  which  being  easily  removed  in  the 
case  of  zinc  or  magnesium,  is  not  very  troublesome.  With  other 
metals  in  general  the  oxidation  is  serious  and  is  rapid  enough  to 
make  operation  unstable  and  inconvenient. 

With  a  given  condenser,  the  quantity  of  electricity  stored  on  the 

plates  at  each  charging  is  proportional  to  the  voltage  impressed 

(Section  30),  and  this  can  be  regulated  by  lengthening  or  shortening 

the  spark  gap  to  obtain  a  higher  or  lower  voltage  at  the  beginning 

97340°— 19 17 


258 


RADIO   COMMUNICATION. 


of  the  discharge.  The  length  of  the  gap  which  can  be  employed  is 
limited  by  the  voltage  that  the  transformer  is  capable  of  producing, 
the  ability  of  the  condenser  dielectric  to  withstand  the  voltage, 
and  the  fact  that  for  readable  signals  the  spark  discharge  must  be 
regular.  If  the  gap  is  too  long,  sparks  will  not  pass,  or  only  at 
irregular  intervals.  The  condenser  is  endangered  also.  If  the  gap 
is  too  short  it  may  arc  and  burn  the  electrodes.  Arcing  causes  a 
short  circuit  of  the  transformer,  and  the  heavy  current  that  flows 
interferes  with  the  high  frequency  oscillations.  An  arc  gives  a 
yellowish  color  and  is  easily  distinguished  from  the  bluish  white, 
snappy  sparks  of  normal  operation.  Even  if  no  arc  takes  place. 


ia 


I8Z 


Plai 


the  voltage  is  reduced  by  using  too  short  a  gap  and  this  results  in 
reduced  power  and  range.  The  length  for  smooth  operation  can 
usually  be  determined  by  trial. 

Quenched  Gap. — It  is  found  that  a  short  spark  between  cool  elec- 
trodes is  quenched  very  quickly,  the  air  becoming  non-conducting 
almost  immediately  after  it  is  broken  down,  or  as  soon  as  the  current 
falls  to  a  low  value.  This  action  is  also  improved,  if  the  sparking 
chamber  is  air  tight.  The  standard  form  of  quenched  gap  consists 
of  a  number  of  flat,  copper  or  silver  discs  of  large  surface,  say  7  cm. 
to  10  cm.  in  diameter  at  the  sparking  surface,  with  their  faces  sepa- 
rated by  about  0.2  mm.  To  provide  the  necessary  total  length  of 


RADIO   COMMUNICATION.  259 

gap  for  high  voltage  charging,  a  number  of  theso  small  gaps  are 
put  in  series,  so  that  the  spark  must  jump  them  all,  one  after  the 
other.  The  discs  are  separated  by  rings  of  mica  or  paper,  see  Fig. 
183.  Fig.  184  shows  a  commercial  type  of  quenched  gap.  The 
motor-driven  blower  attached  serves  to  keep  the  discs  cool.  They 
are  usually  made  with  projecting  fins  for  radiating  the  heat,  and  in 
one  design  air  spaces  are  provided  between  the  pairs  of  discs  which 
form  the  successive  gaps.  The  number  of  gaps  is  determined  by 
the  voltage,  allowing  about  1200  volts  for  each  gap.  Eight  or  ten 
gaps  are  usually  sufficient. 

The  quenched  gap  is  not  used  in  sets  having  a  supply  frequency 
as  low  as  GO  cycles  per  second.  The  sparks  obtained  at  that  fre- 
quency are  found  to  be  irregular  and  not  of  good  tone.  For  this 
case  a  rotary  gap  is  used,  as  explained  below.  For  500-cycle  supply 
the  quenched  gap  is  adjusted  to  break  down  at  the  maximum  value 
of  the  applied  voltage;  that  is,  with  its  total  length  so  adjusted  as 
to  give  one  spark  for  each  half  cycle  of  the  emf.  See  Fig.  185. 
Discharges  at  other  times  are  not  possible,  and  as  a  result  of  this 
regularity  a  clear  note  is  obtained.  This  quenched  gap  is  con- 
sidered as  standard  for  power  up  to  about  10  kw.  One  advantage 
of  the  quenched  gap  not  previously  explained,  is  that  it  aids  the 
production  of  a  so-called  pure  wave.  This  is  discussed  in  Section 
163.  It  has  also  the  advantage  of  being  noiseless,  on  account  of  the 
very  short  gaps  and  the  enclosure  of  the  spark. 

Rotary  Gap. — A  rotary  gap  consists  of  a  wheel  with  projecting 
points  or  knobs,  with  a  stationary  electrode  on  each  side  of  the  wheel. 
See  Fig.  186.  The  spark  jumps  from  one  stationary  electrode  to  one 
of  the  moving  points,  flows  across  the  wheel,  and  then,  after  leaping 
the  corresponding  gap  on  the  other  side,  passes  out  at  the  second  sta- 
tionary electrode.  The  number  of  sparks  per  second  is  thus  deter- 
mined by  the  speed  of  the  wheel  which  is  motor  driven  so  that  signals 
of  high  pitch  can  be  produced.  For  a  modified  form  of  rotary  gap 
see  Fig.  187.  An  advantage  of  the  rotary  gap  is  its  prevention  of 
arcing,  because  of  its  motion  and  the  fanning  action,  and  because 
the  electrodes  brought  successively  up  to  the  spark  gap  have  time 
to  cool  in  their  idle  intervals. 

In  the  case  of  a  "synchronous"  rotary  gap  the  speed  is  so  main- 
tained as  to  bring  the  knobs  near  together  at  just  the  moment  when 
the  alternating  voltage  upon  the  condenser  reaches  its  maximum 
value,  positive  and  negative.  Thus  500  cycles  will  produce  1000 


260 


RADIO    COMMUNICATION, 


FIG.  184.— Radio  telegraph  transmitting  and  receiving  set,  type  SCR-49  (pack  set), 
showing  quenched  spark  gap  in  back  left  corner  of  box. 


RADIO   COMMUNICATION. 


261 


sparks  a  second.  This  regular  occurrence  of  the  discharges  gives 
smooth  and  efficient  operation,  and  a  pure  musical  tone.  The 
synchronizing  is  made  possible  by  attaching  the  rotating  element 


PIG.  185 


One  S)aarK   ^«.r 
hi  If  cycle  with 


of  the  spark  gap  to  the  shaft  of  the  generator  which  charges  the  con- 
denser.    A  rotary  gap  not  so  timed  is  called  '  'non-synchronous.  " 

Attempts  to  produce  a  high  pitch  from  a  60-cycle  source  by  a 
synchronous  gap  giving,  say,  exactly  6  sparks  per  half  cycle,  have 
not  given  satisfaction,  because  the  applied  voltage  is  not  the  same 
at  the  time  of  the  different  sparks,  and  while  the  note  is  of  high 


Fie. 


ROTARY    SPAXK     GAP 


pitch,  it  is  not  musical.  It  has  been  found  better  to  use  a  non- 
synchronous  gap  in  such  a  case,  producing  a  large  number  of  sparks 
per  second  and  letting  them  occur  wherever  they  may  happen 


262 


RADIO    COMMUNICATION. 


during  the  cycle.  The  irregularities  will  somewhat  balance  up. 
While  the  tone  is  not  strictly  musical,  it  can  be  made  of  high  pitch. 
The  non-synchronous  gap  is  best  used  if  nothing  but  a  60-cycle  or 
other  low  frequency  source  is  available.  Such  a  low  frequency, 
however,  is  being  avoided  in  modern  apparatus.  The  standard 
frequency  is  500  cycles  per  second  at  present,  although  there  is  a 
decided  tendency  toward  the  adoption  of  900  cycles  per  second. 

The  plain  spark  gap  is  not  now  used  except  in  small  sets;  quenched 
or  rotary  gaps  are  the  rule.  The  plain  gap  cannot  be  properly  de- 
ionized  to  allow  the  condenser  to  recharge,  and  it  is  very  difficult,  or 
impossible,  to  prevent  arcing  when  large  power  is  used,  especially 
with  a  large  number  of  sparks  per  second,  as  in  modern  practice.  As 
regards  the  choice  between  the  quenched  and  rotary  gaps  the  rotary 


PIG.  187 


Rotor 


Rotary  S^arK  ^  with  1>'o 
rotating  electrodes 


does  not  find  favor  because  it  is  very  noisy.  Another  objection  to 
the  rotary  gap,  for  use  on  airplanes,  is  that  when  the  gap  is  driven 
i>y  a  small  airfan,  the  tone  given  by  the  radio  transmitter  varies  with 
every  change  of  speed  or  direction  of  the  airplane. 

157.  Simple  Induction  Coil  Set.— For  short  distance  communica- 
tion in  trenches,  and  in  general  for  power  below  £  kw.,  it  is  common 
to  use  an  induction  coil  or  a  power  buzzer  instead  of  an  alternator 
and  transformer,  to  charge  the  condenser.  The  wiring  of  an  induc- 
tion coil  is  shown  in  Fig.  188.  P  is  the  primary  coil  of  a  few  turns 
(heavy  lines);  S  is  the  secondary  of  many  turns  of  fine  wire;  /is  an 
iron  core  magnetized  by  the  primary  current;  and  if  is  a  piece  of 
soft  iron  at  the  end  of  a  spring  forming  a  sort  of  vibrating  hammer; 
H  is  an  adjusting  screw  for  the  vibrator;  C  is  a  condenser  of  a  few 


RADIO    COMMUNICATION.  263 

microfarads  shunted  around  the  vibrator  points  to  prevent  their 
burning.  The  vibrator  points  may  be  replaced  when  necessary  by 
drilling  a  hole  and  driving  in  a  piece  of  silver.  V shows  the  vibrator 
points  where  the  primary  current  is  made  and  broken  in  rapid 
succession  as  long  as  the  key  K  is  closed.  When  current  flows,  H 
is  first  attracted,  breaking  the  current  at  V  after  which  the  spring 
causes  it  to  return  to  its  first  position,  remaking  the  current.  The 
action  is  then  repeated.  The  frequency  of  operation  depends  upon 
the  mass  of  the  hammer  H  and  the  stiffness  and  length  of  the  spring. 
It  is  similar  in  that  respect  to  an  electric  bell.  This  piece  of  ap- 
paratus is  really  an  open  core  transformer,  the  changes  of  current 
being  produced  by  the  automatic  interrupter  or  vibrator,  which  is 
operated  by  the  magnetism  of  the  core.  The  source  of  power  is 
usually  a  storage  battery  of  8  to  20  volts.  Owing  to  the  changes  of 
primary  current,  rapid  changes  of  magnetic  flux  occur  and  produce 
a  high  voltage  in  the  large  number  of  turns  of  the  secondary  coil. 

Referring  again  to  Fig.  180,  consider  the  induction  coil  put  in 
place  of  the  a.c.  transformer.  When  the  coil  is  put  into  operation, 
with  its  secondary  terminals  connected  to  the  condenser  and  dis- 
charge circuit,  a  continuous  stream  of  sparks  will  pass  across  the 
spark  gap  as  long  as  the  key  is  pressed. 

158.  Operation  of  Induction  Coils  from  Power  Lines. — Fairly  large 
power  induction  coil  sets  are  used  as  emergency  transmitters  on 
ships.  These  employ  batteries,  so  as  to-be  independent  of  the 
ship's  generator.  On  land,  however,  when  a  battery  is  not  avail- 
able, it  is  possible  to  operate  an  induction  coil  from  a  d.c.  110-volt 
power  line  by  inserting  a  rheostat  in  series.  In  this  case,  it  is 
absolutely  necessary  to  shunt  the  transmitting  key  with  a  condenser 
similar  to  the  vibrator  condenser,  or  else  a  serious  arc  at  the  key  will 
take  place  at  the  first  attempt  to  signal,  and  the  current  will  not  be 
broken  when  the  key  is  released.  Of  course,  the  method  of  insert- 
ing a  rheostat  is  very  wasteful,  as  the  RI2  loss  in  the  rheostat  is  large, 
much  greater  in  fact,  than  the  power  actually  used  in  the  radio 
apparatus. 

A  scheme  to  avoid  a  voltage  as  high  as  the  110  volts  across  the 
break  at  the  key  is  to  use  a  voltage  divider  consisting  of  two  rheostats 
in  series,  as  in  Fig.  189.  Suppose  the  spark  coil  has  2  ohms  resistance 
in  the  primary,  and  requires  10  volts  to  operate  it.  If  one  rheostat 
is  set  at  10  ohms  and  the  other  at  2  ohms,  with  the  induction  coil 
and  key  in  a  shunt  around  the  2-ohm  coil,  then  the  voltage  applied 


264 


RADIO    COMMUNICATION. 


to  the  induction  coil  will  be  10  volts  with  the  key  closed.  Note 
that  the  voltage  across  the  key  when  open  is  18.3  volts. 

With  a.c.  supply  the  methods  are  different.  One  method  of  oper- 
ating an  induction  coil  from  110  volts  a.c.  is  to  use  a  small,  step- 
down  transformer  to  reduce  the  voltage  to  an  equivalent  battery 
voltage.  This  requires  no  series  resistance  or  reactance,  and  is  a 
fairly  efficient  method.  Induction  coils  are  sometimes  operated  on 
110- volt  a.c.  power  lines  by  insertion  of  a  series  reactance.  The 
vibrator  in  the  primary  circuit  is  not  necessary  if  the  supply  is  500- 
cycle,  and  it  is  preferable  to  clamp  it  permanently  in  the  closed 
position.  The  set  then  becomes  similar  to  Fig.  180.  Induction 
coils  may  have  the  primary  wound  for  110  volts,  in  which  case  no 
transformer  nor  series  reactance  or  resistance  is  needed. 

159.  Portable  Transmitting  Sets. — For  portable  sets,  or  for  Army 
field  use  the  simplest  apparatus  for  short  distances  is  a  small  induc- 


Fia 


Induction  coil  on 
d-c.  JDow«.r   h' 
(Secondary  ci 
not  •shown) 


.  g  1 

'ower    buyysr  circuit       I 


tion  coil  set,  operated  from  a  storage  battery.  A  plain  spark  gap 
may  be  used,  for  simplicity,  but  the  use  of  a  quenched  gap  will 
usually  improve  the  operation.  When  fairly  long  distances  are  to 
be  covered  it  is  advisable  to  replace  the  induction  coil  by  a  small 
step-up  transformer.  A  source  of  alternating  current  then  takes  the 
place  of  the  battery .  For  a  small  set  this  source  may  be  a  generator 
which  is  driven  by  hand  through  gearing.  For  larger  power  the  gen- 
erator may  be  driven  by  the  engine  of  a  motorcycle  or  some  other 
gasoline  engine. 

For  short  distance  work  the  condenser  may  be  charged  and  radio 
oscillations  produced,  without  an  induction  coil,  by  the  use  of  a 
power  buzzer  and  a  storage  battery  or  a  few  dry  cells.  See  Fig.  190. 
The  buzzer  is  shown  at  Z .  The  more  voltage  applied  to  it  the  greater 


RADIO    COMMUNICATION.  265 

is  the  charge  given  to  the  condenser  C.  When  the  vibrator  arm  is 
at  the  right  in  the  diagram,  the  condenser  discharges  through  the 
inductance  L.  This  forms  the  closed  oscillating  circuit.  The  con- 
denser should  be  comparatively  small;  the  apparatus  is  limited  to 
short  wave  lengths. 

For  very  short  distances  the  more  common  military  practice  is  to 
use  "ground  telegraphy"  or  "T.P.S."  (telegraphic  par  sol)  in- 
stead of  radio.  For  the  theory  and  practical  application  of  ground 
telegraphy,  which  uses  no  wires  between  the  two  points  of  commu- 
nication, see  Radio  Pamphlets  Nos.  10,  15,  and  18. 

1GO.  Simple  Connections  for  the  Production  of  Electric  Waves. — 
Up  to  this  point,  have  been  shown  the  means  by  which  an  oscillating 
discharge  is  produced  in  a  condenser  circuit.  It  is  necessary  now 
to  learn  how  the  oscillations  can  be  gotten  into  an  antenna  so  they 
may  be  sent  out  as  radio  waves.  The  wiring  connections  for  the  dif- 
ferent methods  are  given  in  this  and  the  following  sections,  showing 
first  the  simplest  transmitting  connections  and  then  leading  up  to 
standard  sets. 

The  simplest  possible  wave  transmitter  is  a  straight  wire  cut  in 
the  middle  by  a  small  spark  gap.  See  Fig.  191.  If  the  wire  were 
not  cut,  and  if  oscillations  could  be  produced  in  it,  the  charges 
would  travel  rapidly  back  and  forth  owing  to  the  capacitance  and 
inductance  of  the  wire  and  waves  would  move  out  into  space  as  ex- 
plained in  Chapter  4.  The  oscillations  taking  place  in  the  wire  are 
of  the  same  nature  as  those  in  the  circuit  CL  of  Fig.  180.  The 
student  should  learn  to  think  of  the  wire  as  uncut,  for  the  gap  be- 
comes a  conductor  when  the  spark  is  passing.  Oscillations  are 
produced  by  the  same  means  described  in  Section  154,  using  a  high 
voltage  to  start  a  discharge  across  the  spark  gap.  This  is  done  by 
connecting  a  transformer  or  an  induction  coil  to  the  gap.  The  use 
of  an  induction  coil  is  shown  in  Fig.  191.  The  two  halves  of  the 
wire  charge  up  as  a  condenser  until  the  potential  difference  rises  so 
high  that  the  insulating  property  of  the  gap  is  broken  down.  There 
is  then  a  discharge  across  the  gaps  and  oscillations  pass  freely  until 
the  energy  is  spent.  The  gap  then  becomes  non-conducting  again 
as  has  been  explained,  and  permits  a  renewed  charging.  The  process 
is  repeated  as  many  times  a  second  as  the  vibrator  works. 

The  interval  from  one  break  at  the  vibrator  to  the  next  may  be 
about  0.01  second,  while  it  will  take  only  in  the  neighborhood  of 
0.00001  second  for  the  discharge  to  be  completely  accomplished 


260 


RADIO    COMMUNICATION. 


(basis  of  illustration  is  a  wave  length  of  150  meters,  20  waves  to  a 
train).  Thus  it  is  seen  that  there  is  a  comparatively  large  time  inter- 
val between  successive  wave  trains,  in  which  the  gap  may  cool  and  be 
restored.  A  sketch  of  the  discharge  current  is  shown  in  Fig.  192,  but 
the  wave  trains  are  not  shown  nearly  far  enough  apart  for  the  case  of 
a  damped  oscillator  such  as  that  of  Fig.  191.  To  show  how  relatively 
large  the  time  interval  between  successive  wave  trains  is,  it  might  be 
stated  that,  in  this  illustration,  the  length  of  the  wave  train  itself 
compares  with  the  length  of  the  idle  interval  between  wave  trains 
about  in  the  same  ratio  as  one  day  compares  with  three  years. 

The  next  theoretical  step  toward  a  standard  radio  transmitting  set 
is  to  add  large  metal  plates  to  the  outer  ends  of  the  straight  wires. 


Fia.  112   rl 


See  Fig.  193.  This  increases  the  capacitance  of  the  oscillator  and 
causes  larger  charges  to  accummulate  for  the  same  potential  differ- 
ence, thus  giving  a  larger  flow  of  current  back  and  forth  in  the  wire  and 
sending  out  more  electric  and  magnetic  lines  of  force.  The  strength 
of  signals  and  the  range  are  thus  increased. 

It  is  shown  in  Section  132  that  the  lower  half  of  the  oscillating 
system,  Figs.  191  or  193,  may  be  replaced  by  the  ground,  the  action 
of  the  upper  half  remaining  as  before.  Also,  it  is  customary  to  re- 
place the  upper  capacitance  plate  of  Fig.  193  by  one  or  more  wires, 


RADIO    COMMUNICATION. 


267 


horizontal  or  nearly  so.  See  Fig.  194.  A  relatively  large  capaci- 
tance can  thus  be  added,  and  the  constructional  difficulties  and 
arrangements  of  support  are  simplified.  This  assemblage  of  wires 
forms  the  " antenna."  A  variable  inductance  coil  inserted  in  the 
antenna  wire  will  permit  tuning  to  different  frequencies  or  wave 
lengths.  Thus  a  simple  transmitting  outfit  is  built  up. 

The  arrangement  shown  in  Fig.  194  is  called  the  plain  antenna 
set  to  distinguish  it  from  the  inductively  coupled  set  explained 
below.  It  is  a  good  radiating  system,  but  the  waves  emitted  are  of 
such  high  decrement  that  they  cannot  be  readily  tuned  out  in 


receiving  apparatus  when  one  does  not  desire  to  receive  them. 
See  Section  116.  Hence  this  system  is  not  permissible  in  general 
practice.  Its  advantages  besides  simplicity  are,  however,  its 
effectiveness  in  cases  where  the  sending  operator  wants  all  possible 
stations  to  hear  him,  as  for  instance  when  a  ship  needs  help,  and 
secondly  its  military  use  in  purposely  drowning  out  or  "jamming" 
other  signals  which  an  enemy  is  trying  to  receive.  The  connection 
is  very  quickly  made  by  inserting  the  spark  gap  directly  between 
the  antenna  and  ground  wires,  and  connecting  the  current  source 
across  the  gap.  Arcing  in  the  gap  must  be  guarded  against,  and  care 


268  RADIO    COMMUNICATION. 

should  be  taken  not  to  open  the  gap  too  wide,  or  the  antenna  insula- 
tion may  break  down. 

161.  Inductively  Coupled  Transmitting  Set. — Instead  of  connect- 
ing the  spark  gap  directly  in  series  with  the  antenna  it  may  be 
placed  in  a  separate  oscillating  circuit  like  that  of  Fig.  180  and  this 
circuit  then  coupled  with  the  antenna.  In  the  most  common 
method  the  coil  of  the  oscillating  circuit  (called  the  "closed  "  circuit 
to  distinguish  it  from  the  open  or  antenna  circuit)  is  coupled  induc- 
tively to  the  inductance  coil  in  series  with  the  antenna.  The  cir- 
cuits thus  become  Fig.  195.  One  of  the  advantages  of  this  method 
is  that  the  condenser  in  the  closed  circuit  may  have  much  greater 
capacitance  than  the  antenna  and  thus  may  store  more  energy  for 
each  alternation  of  the  supply  voltage;  this  energy  is  handed  over 
to  the  antenna  which  thus  becomes  a  more  powerful  radiator. 
Other  features  of  the  method  are  given  in  Section  163  below. 

As  before,  either  an  induction  coil  or  a  transformer  with  a.c.  supply 
voltage  may  be  used.  In  Fig.  195  the  latter  is  shown.  T  is  an  iron 
core  transformer,  somewhat  similar  in  construction  to  the  ordinary 
transformer  used  in  electric  light  systems.  The  two  inductance 
coils  P  and  8  constitute  what  is  sometimes  called  an  "oscillation 
transformer."  A  hot  wire  ammeter  is  in  series  with  the  antenna. 
The  positions  of  the  spark  gap  and  condenser  are  sometimes  inter- 
changed, bringing  the  spark  gap  across  the  transformer.  See  Fig.  196. 
There  is  no  practical  difference  in  the  operation. 

The  condenser  discharge  cannot  take  place  through  the  trans- 
former T  on  account  of  its  very  great  impedance,  but  passes  across 
the  spark  gap  and  through  the  few  turns  of  the  primary  coil  P,  pro- 
ducing a  rapidly  changing  magnetic  flux  within  the  coil.  The 
secondary  coil  8  is  placed  near  or  inside  of  coil  P,  so  that  part  of  the 
alternating  magnetic  flux  of  P  passes  through  8.  There  are  three 
principal  styles  of  oscillation  transformer,  the  double  helix,  hinged 
coil,  and  flat  spiral  types.  See  Figs.  197,  198,  199.  In  order  to 
have  a  low  resistance  the  conductor  is  usually  a  copper  ribbon  of 
large  surface,  or  edgewise  wound  copper  strip.  The  amount  of 
coupling,  or  the  mutual  inductance,  between  them  is  varied  by 
moving  one  or  both  of  the  pair.  Connections  are  made  to  such 
coils  by  movable  clips,  so  that  any  desired  amount  of  self  inductance 
may  be  used. 

The  hot  wire  ammeter  is  used  for  measuring  the  current  in  the 
antenna  circuit.  For  merely  tuning  to  resonance  a  low  resistance 


RADIO    COMMUNICATION. 


269 


lamp  such  as  a  small  flashlight  lamp  may  be  used  in  place  of  the 
hot  wire  ammeter,  the  maximum  current  being  indicated  by  the 


FIG.  197.— Double  helix  oscillation  transformer;  coils  separated  axially. 


maximum  brightness  of  the  lamp  filament.    If  the  current  is  too 
great  for  the  lamp  it  should  be  shunted  by  a  short  length  of  wire. 


270 


RADIO    COMMUNICATION. 


The  ammeter  or  lamp  may  be  short  circuited  except  when  actually 
needed,  in  order  to  keep  the  resistance  of  the  antenna  circuit  low. 
1G2.  Direct  Coupled  Transmitting  Set. — Direct  instead  of  induc- 
tive coupling  may  be  used  between  the  closed  circuit  and  the 
antenna  circuit,  as  in  Fig.  200.  (Direct  coupling  was  explained 
in  Sec.  119).  One  inductance  coil  is  all  that  is  needed.  By  the 
contacts  shown,  as  much  or  as  little  of  the  inductance  as  desired 


FIG.  198. — Hinged  coil  oscillation  transformer. 

can  be  used  in  either  circuit.  In  order  to  tune  to  some  wave  lengths 
it  may  be  necessary  to  have  an  additional  coil  in  series  in  the  closed 
circuit.  By  making  the  part  of  the  inductance  that  is  common  to 
both  circuits  a  small  part  of  the  total  inductances  in  the  circuits, 
the  coupling  can  be  made  as  loose  as  desired.  Since  direct  and 
inductive  coupling  are  strictly  equivalent,  the  discussion  of  one 
applies  to  both. 


RADIO    COMMUNICATION. 


271 


163.  Comparison  of  Coupled  and  Plain  Antenna  Sets. — In  the 

plain  antenna  set  of  Fig.  194  the  spark  gap  is  in  series  with  the 
antenna.  Thus  the  resistance  of  the  gap  is  present  and  helps  to 
make  the  decrement  of  the  radiated  waves  high.  While  high  decre- 
ment is  an  advantage  in  special 
cases,  as  explained  in  Section 
160,  it  is  usually  not  desirable. 
When  the  spark  gap  is  in  a  sep- 
arate circuit,  coupled  either  in- 
ductively or  directly  to  the  an- 
tenna, as  in  Figs.  195  or  200, 
the  resistance  of  the  spark  gap 
does  not  enter  into  the  antenna 
resistance.  The  decrement  of 
the  wave  sent  out  by  the  set 
is  subject  to  control.  The  con- 
denser in  the  closed  circuit 
may  have  large  capacitance  and 
thus  store  a  great  amount  of 
energy  and,  if  a  plain  spark  gap  is  used,  produce  a  discharge  that 
persists  a  relatively  long  time  before  dying  away.  This  oscillating 
current  in  the  closed  circuit  forces  oscillations  in  the  antenna  of 
the  same  small  decrement. 


"Flat  Spiral  Type 
Oscillation  Transformer. 


FIG  Zoo 


When  a  quenched  gap  is  used,  it  would  make  the  decrement  much 
worse  if  used  in  the  antenna  circuit.  When  used  in  the  closed  cir- 
cuit, however,  the  oscillations  in  the  closed  circuit  have  such  a  high 


272  RADIO    COMMUNICATION. 

decrement  that  they  stop  almost  immediately,  and  simply  start  the 
antenna  circuit  oscillating,  which  thereafter  oscillates  with  its  nat- 
ural decrement  which  may  be  small. 

On  account  of  the  small  decrement  of  the  oscillations  in  the 
antenna  circuit  the  instantaneous  voltages  do  not  reach  as  high 
values,  with  a  given  current  and  power  output,  as  they  do  when 
the  oscillations  are  strongly  damped.  Thus  the  voltages  in  the 
antenna  are  not  as  great,  when  the  coupled  circuit  is  used,  and  the 
antenna  insulators  are  not  as  likely  to  fail. 

164.  Tuning  and  Resonance. — A  Very  pronounced  maximum  of 
current  is  obtained  in  the  antenna  circuit  when  its  natural  period  of 
oscillation  is  the  same  as  that  of  the  primary  circuit.     This  occurs 
when  LSCS=LPCP.     (See  Chapter  3,  Section  116).     Ls  is  the  induc- 
tance of  the  antenna  circuit,   including  the  antenna  itself,  lead-in 
wire  and  the  secondary  coil  of  the  air  core  transformer.     Cs  is  the 
capacitance  of  the  same  circuit.     Lp  is  the  inductance  of  the  primary 
circuit,  and  since  the  wiring  is  short  the  inductance  is  nearly  all  in 
the  coil  L.     Likewise,  since  C  has  a  large  capacitance,  Cp  is  practi- 
cally the  capacitance  of  this  condenser.     It  is  not  necessary  in  oper- 
ation to  measure  any  of  these  quantities.     The  hot  wire  ammeter 
will  show  by  trials  when  the  products  are  equal,  or  a  wavemeter  will 
enable  the  operator  to  adjust  each  circuit  P  and  S  to  the  same  fre- 
quency, or  to  any  desired  wave  length.     The  principal  case  where 
the  inductances  and  capacitances  need  to  be  known  is  in  the  design 
of  a  set  which  differs  from  previous  sets  so  much  that  the  proper  size 
of  apparatus  is  not  known.    To  adjust  the  apparatus  to  send  out  long 
waves,  a  large  inductance  may  be  used  in  series  with  the  antenna. 
It  is  preferable,  however,  to  use  a  large  antenna  thus  obtaining  large 
capacitance,  which  stores  up  large  charges  and  allows  a  large  radi- 
ating current. 

165.  Coupling. — When  the  antenna  and  closed  circuits  are  adjusted 
independently  to  the  same  frequency  or  wave  length,  and  then 
closely  coupled  together,  waves  of  two  frequencies  appear  in  each 
circuit.     See  Section  120.     For  showing  the  double  wave  in  radio 
apparatus,  a  wavemeter  (see  Section  112)  placed  near  either  of  these 
coupled  radio  circuits  will  be  found  to  indicate  a  maximum  response 
at  two  different  wave  lengths.     If  then  the  coupling  between  the 
two  circuits  is  diminished,  the  two  wave  lengths  approach  each  other 
and  the  wave  length  for  which  the  circuits  were  set,  and  at  a  very 
loose  coupling  only  one  wave  length  will  be  discernible.     Figs.  201 


RADIO    COMMUNICATION. 


273 


to  204  show  resonance  curves  for  the  case  where  the  primary  and 
secondary  are  adjusted  separately  to  600  meters,  and  then  are  coupled 
by  bringing  the  secondary  and  primary  coils  near  together  (when 
the  coupling  is  inductive).  When  the  coupling  is  direct  it  is  made 
closer  by  making  a  larger  part  of  the  inductance  of  each  circuit  com- 
mon to  both  circuits.  These  effects  are  more  pronounced  when  a 
plain  or  rotary  rather  than  a  quenched  gap  is  used. 

Fig.  201  might  allow  of  fairly  sharp  tuning  on  one  of  the  wave 
lengths,  but  only  the  energy  of  one  wave  could  be  utilized  by  a  re- 
ceiving apparatus.  Figs.  202  and  203  would  be  the  equivalent  of  a 


Fiq.207 


M«fer» 


Resonance  corve.Goils 

little. 


Matere 


e  curve,  coi  Is  Sefrr&d  -f  urThe 


rxce  corv«,  very  Ux»s« 


single  wave  of  very  broad  shape  or  high  decrement,  such  that  the 
strength  of  the  signals  is  nearly  the  same  over  a  wide  range  of  wave 
lengths.  In  Fig.  204  the  signals  are  strong  at,  or  near,  only  one  wave 
length,  and  diminish  rapidly  if  any  of  the  apparatus  adjustments  are 
changed.  This  is  said  to  be  a  "pure "  wave.  It  is  desirable  to  have 
as  sharp  a  resonance  curve  as  possible,  and  hence  loose  coupling  is 
the  rule  when  a  plain  gap  is  used.  The  advantage  is  that  all  the 
power  sent  out  is  concentrated  into  a  narrow  range  of  wave  lengths,, 
and  that  receiving  stations  can  tune  to  one  wave  which  they  desire 
to  receive  at  and  not  receive  others. 
97340°— 19 18 


274  RADIO    COMMUNICATION. 

Action  of  the  Quenched  Gap;  Relation  to  Coupling. — Refer  again  to 
the  inductively  coupled  apparatus  of  Fig.  195  and  to  the  waves  of 
Fig.  154  in  Chapter  3.  Also  refer  to  the  description  of  the  quenched 
gap  in  Section  156.  The  action  of  the  quenched  gap  is  to  open  the 
primary  circuit,  by  suppression  of  the  spark  at  the  end  of  its  first 
train  of  waves  (point  D  in  Fig.  154).  This  prevents  the  secondary 
from  inducing  oscillations  in  the  primary  again,  that  is,  from  giving 
energy  back  to  the  primary.  The  secondary  or  antenna  oscillations 
.•are  not  thereafter  interfered  with  by  the  primary  and  the  antenna 
;goes  on  oscillating  until  the  energy  is  all  dissipated  as  waves  or 
Jieat  (see  Fig.  155).  The  length  of  the  train  will  depend  only  upon 
the  decrement  of  the  antenna  circuit.  By  reducing  the  resistance, 
the  dielectric  losses,  the  brush  discharges  and  leakage,  the  antenna 
current  may  be  made  to  oscillate  for  a  comparatively  long  time,  at 
the  frequency  for  which  the  set  was  adjusted.  This  quenching  of  the 
primary  avoids  the  double  waves  of  Figs.  201,  202  and  203,  even  with 
close  coupling.  In  fact,  the  coupling  should  be  close  for  good  oper- 
ation with  the  quenched  gap.  Some  care  has  to  be  taken  in  the 
adjustment  of  the  coupling,  but  when  adjusted  properly  this  gap 
gives  a  high  pitched,  clear  note.  The  wavemeter  will  readily  show 
when  a  single  sharp  wave  is  obtained  (see  Section  168),  and  the  sound 
in  the  telephone  receiver  will  indicate  the  proper  adjustment  for 
good  tone.  The  quenched  gap  is  very  efficient,  because  the  close 
coupling  produces  a  large  current  in  the  antenna. 

It  is  well  to  note  that  the  principles  of  operation  of  the  quenched 
gap  and  plain  gap  are  exactly  opposite.  The  former  aims  to  stop 
the  primary  oscillations  quickly,  after  the  secondary  has  been 
brought  to  full  activity.  The  latter  aims  to  keep  the  primary 
oscillations  going  as  long  as  possible,  all  the  time  giving  energy  to 
the  secondary  as  it  is  radiated  away;  the  coupling  is  loose  and 
the  primary  decrement  is  kept  low.  The  rapid  decrease  of  the 
oscillations  in  a  quenched  gap  circuit  are  assisted  by  having  a  large 
ratio  of  capacitance  to  inductance.  This  has  the  incidental  advan- 
tage that  the  voltages  across  the  condenser  and  coil  are  thus  kept 
low. 

166.  Damping  and  Decrement. — If  the  energy  in  the  antenna  cir- 
cuit is  dissipated  at  too  rapid  a  rate,  owing  either  to  radiated  waves 
or  heat  losses,  the  oscillations  die  out  rapidly  and  not  enough  waves 
exist  in  a  received  train  to  set  up  oscillations  of  a  well  defined  period 
in  a  receiving  antenna.  Such  waves  are  strongly  damped  and  have 


RADIO   COMMUNICATION.  275 

a  large  decrement.  They  produce  received  currents  of  about  the 
same  value  for  a  considerable  range  of  wave  lengths.  Thus  selec- 
tive timing  is  not  possible.  To  increase  the  number  of  waves  sent 
out  in  each  wave  train  from  the  open  circuit  (that  is,  to  make  the 
oscillations  last  longer)  the  resistance  of  the  circuits  must  be  kept 
low.  When  using  a  plain  spark  gap  the  coupling  between  closed 
and  antenna  circuits  must  be  small  enough  not  to  take  energy  too 
fast  from  the  closed  oscillating  circuits.  At  each  condenser  discharge 
the  primary  has  a  train  of  oscillations  which  at  best  die  out  long 
before  another  train  starts  (see  Fig.  192);  these  oscillations  are 
stopped  more  quickly,  however,  if  the  energy  is  drawn  rapidly  out 
of  the  circuit  by  the  antenna.  Close  coupling  is  permissible  only 
when  a  quenched  gap  is  used,  (see  remarks  at  the  end  of  the  pre- 
ceding section.)  With  any  other  kind  of  gap  the  secondary  is  kept 
oscillating  by  energy  continually  received  from  the  primary. 

A  great  many  factors  contribute  to  the  resistance  of  the  antenna 
circuit,  and  this  must  be  kept  as  low  as  possible.  The  antenna 
must  have  a  good,  low  resistance  ground,  must  use  wires  of  fairly 
low  resistance,  and  must  not  be  directly  over  trees  or  other  poor 
dielectrics.  The  resistance  of  the  closed  circuit  particularly  must 
be  very  low.  Heavier  currents  flow  here  than  in  the  antenna  wires. 
For  this  reason  the  closed  circuit  wires  should  be  short  and  of  large 
surface,  preferably  stranded  wires  or  copper  tubing.  The  condenser 
should  be  a  good  one,  free  from  power  loss. 

167.  Additional  Appliances. — A  number  of  additional  appliances 
are  necessary  or  desirable  for  the  operation  of  a  damped  wave  gener- 
ating set.  The  operation  is  improved  by  having  a  variable  reactance 
(iron  core  inductor)  in  series  with  the  alternator,  to  tune  the  alter- 
nator circuit  to  the  alternator  frequency.  See  C.  74,  p.  230. 

Changes  of  Wave  Length. — In  many  sets  of  apparatus  it  is  cus- 
tomary to  have  connections  arranged  by  means  of  which  different 
chosen  wave  lengths,  say  300  or  600  meters,  can  be  transmitted  with- 
out the  necessity  of  a  readjustment  of  the  apparatus  after  each 
change.  An  antenna  alone  without  any  inductance  coil  has  a  natural 
wave  length  of  its  own,  dependent  upon  its  inductance  and  capaci- 
tance. See  Sections  116  and  145.  The  antenna  is  usually  so  designed 
that  its  natural  wave  length  is  shorter  than  the  wave  length  to  be 
used,  and  the  wave  length  is  brought  up  by  adding  inductance  in 
series  or  merely  by  the  added  inductance  of  the  secondary  of  the 
oscillation  transformer.  In  the  case  of  a  small  antenna  such  as 


276 


RADIO    COMMUNICATION. 


that  on  a  small  ship,  it  is  necessary  to  use  a  large  inductance.  Since 
it  is  desirable  to  have  the  coupling  loose,  a  part  of  the  secondary 
inductance  can  be  in  a  separate  coil  called  the  antenna  "loading 
coil."  This  is  coupled  to  the  primary.  Fig.  205  shows  this  arrange- 
ment. For  a  quick  change  of  wave  length  a  single  switch  is  often 
provided,  which,  by  a  mechanism  of  levers,  changes  simultaneously 
the  adjustments  on  all  three  coils.  From  these  coils  are  taken  out 
taps  over  which  three  switch  blades  pass  adjusting  all  the  induc- 
tances to  approximately  the  values  needed  for  the  particular  wave 
length  desired,  keeping  the  circuits  in  resonance  and  at  the  proper 
coupling.  For  fine  adjustments  an  additional  variable  inductor 
may  be  provided  in  the  primary  and  in  the  secondary. 

Fig.  205  also  shows  an  arrangement  whereby  the  operator  can  ob- 
tain wave  lengths  shorter  than  the  natural  wave  length  of  the  antenna 


Fiq.  105 


by  inserting  a  condenser  in  series,  (see  Section  35),  in  the  antenna 
circuit.  In  this  case  the  loading  coil  will  be  set  at  zero  turns  to  di- 
minish the  wave  length.  The  condenser  inserted  must  be  capable 
of  withstanding  high  voltages  similar  to  those  in  the  main  trans- 
mitting condenser.  By  using  a  small  capacitance  the  wave  length 
can  be  reduced  to  approach  one-half  of  the  natural  wave  length. 
It  should  not  be  reduced  that  much,  however,  for  the  radiation  is 
inefficient  if  the  condenser  is  too  small.  A  zero  capacitance  (an 
open  circuit  cutting  off  the  antenna  entirely  from  the  ground) 
would  be  necessary  to  produce  half  wave  length  exactly. 

Choke  coils. — Fig.  205  shows  also  choke  coils  to  prevent  the  high 
frequency  condenser  discharge  from  getting  into  the  transformer 
and  puncturing  the  insulation.  The  coils  choke  down  the  radio  fre- 
quency current  but  do  not  obstruct  the  low  frequency  charging 


RADIO   COMMUNICATION.  277 

current  from  the  transformer.  They  must  be  specially  designed  so 
that  they  do  not  have  capacitance  enough  to  allow  the  radio  fre- 
quency current  to  pass.  They  can  often  be  dispensed  with. 

168.  Adjustment  of  a  Typical  Set  for  Sharp  Wave  and  Radiation. — 
The  set  is  assumed  to  be  an  inductively  coupled  set,  arranged  as 
in  Fig.  205.  The  first  step  in  adjusting  it  to  work  properly  is  to  tune 
the  closed  circuit  to  the  wave  length  which  is  to  be  used.  This  is 
done  by  the  aid  of  a  wavemeter  having  in  its  circuit  a  sensitive  hot 
wire  ammeter.  The  wavemeter  is  placed  at  a  distance  of  one  or 
more  meters  from  the  coil  of  the  closed  circuit,  and  with  the  set  in 
operation  but  the  antenna  circuit  opened,  the  wavemeter  coil  is  so 
turned  that  a  small  current  is  observed  in  the  wavemeter  ammeter. 
With  the  wavemeter  set  at  the  chosen  wave  length  the  closed  cir- 
cuit inductance  is  varied  until  resonance  is  obtained.  If  no  reso- 
nance point  is  found  it  is  probable  that  the  closed  circuit  inductance 
or  capacitance  is  either  too  large  or  too  small.  This  inductance 
should  be  varied  and  a  resonance  point  will  be  located  after  a  few 
trials. 

The  next  process  is  to  adjust  the  coupling  to  obtain  a  pure,  sharp 
wave,  that  is,  to  get  as  much  of  the  power  as  possible  into  the  wave 
length  that  is  to  be  used.  With  both  antenna  and  closed  circuits 
closed,  the  coupling  between  them  is  varied.  If  the  spark  gap  is  not 
a  quenched  gap,  the  coupling  is  first  made  fairly  loose  and  the  antenna 
loading  coil  is  varied  until  resonance  is  obtained,  as  observed  on  the 
hot  wire  ammeter  in  series  with  the  antenna.  The  coupling  is  then 
made  closer  until  two  points  of  resonance  appear.  It  is  desirable 
to  have  a  pure  wave,  that  is,  have  only  one  resonance  point.  There- 
fore the  coupling  is  loosened  until  it  is  certain  that  there  is  just  one 
sharp  point  of  resonance.  If  the  set  has  a  quenched  gap,  the  coup- 
ling is  kept  close,  and  varied  only  enough  to  insure  a  single,  sharp 
wave. 

It  is  necessary  next  to  adjust  the  apparatus  to  give  maximum 
current.  Keeping  the  wave  length  and  coupling  adjustments 
fixed,  vary  the  voltage  and  length  of  the  spark  gap  and  the  induc- 
tance in  series  with  the  alternator  until  a  good  clear  spark  tone  and 
maximum  current  in  the  antenna  circuit  are  obtained.  It  is  desir- 
able to  repeat  the  coupling  adjustment  and  then  this  adjustment 
again.  When  the  set  has  a  quenched  gap,  best  operation  is  usually 
obtained  when  the  inductance  in  series  with  the  alternator  (Sectior 
167)  is  somewhat  greater  than  that  required  for  resonance  to  the 
alternator  frequency. 


278  RADIO    COMMUNICATION. 

169.  Efficiency  of  the  Set.— To  maintain  good  efficiency,  all  resist- 
ances in  the  circuits  must  be  kept  as  low  as  possible.  A  number  of 
suggestions  for  keeping  resistances  low  were  given  in  Section  166. 
It  is  also  necessary  to  avoid  brush  discharges  and  arcs,  to  keep  all 
connections  tight,  condenser  plates  and  other  parts  of  circuits  free 
from  dust  and  moisture,  and  antenna  well  insulated.  Brush  dis- 
charges may  be  reduced  by  eliminating  sharp  points  or  edges  on 
conductors,  or  by  coating  the  edges  of  metal  plates  with  paraffin. 
The  guy  wires  of  the  antenna  should  be  divided  into  short  lengths 
with  insulators  between  them,  to  reduce  the  flow  of  current  in  them. 
The  inductance  coils  and  the  spark  gap  must  be  properly  designed. 

The  efficiency  may  be  denned  as  the  ratio  of  the  power  radiated 
away  as  electric  waves  from  the  antenna  to  the  power  input  in  the 
transformer.  The  power  input  P  in  the  transformer  may  be  meas- 
ured by  an  ordinary  wattmeter.  The  power  radiated  from  the 
antenna  can  be  expressed  in  the  form  RI2  where  /  is  the  current 
in  the  ammeter  at  the  base  of  the  antenna  and  R  is  the  radiation 
resistance.  The  efficiency  is  then  RI2  divided  by  P.  As  explained 
in  Section  143,  the  radiation  resistance  cannot  be  measured  directly, 
but  can  be  found  from  the  total  effective  antenna  resistance  by 
subtracting  those  resistances  which  give  rise  to  heat  losses. 

Representative  values  for  the  efficiency  of  the  entire  set  are  2 
per  cent  to  15  per  cent.  The  transformer  efficiency  may  be  roughly 
85  per  cent  to  95  per  cent.  The  closed  oscillation  circuit  losses  are 
very  large  in  proportion  to  the  power  transferred,  a  fair  value  of 
efficiency  being  about  25  per  cent  (by  careful  design  and  adjust- 
ment using  the  quenched  gap  this  may  sometimes  be  increased  to 
50  per  cent).  The  efficiency  of  the  antenna  circuit  (radiated  power 
divided  by  power  given  to  the  antenna)  may  be  between  20  per 
cent  and  2  per  cent  or  lower,  or  may  be  made  as  high  as  50  per  cent  if 
special  pains  are  taken.  The  product  of  the  three  separate  percent- 
ages gives  the  over  all  efficiency.  For  an  interesting  table  of  com- 
parative values  of  efficiencies,  see  J.  A.  Fleming's  "Wireless  Teleg- 
raphist's Pocket  Book,"  pp.  221  and  223. 

170.  Calculations  Required  in  Design.— This  section  gives  methods  for  determin- 
ing the  values  of  condensers  and  coils  to  be  used  in  transmitting  apparatus,  and 
enables  one  to  calculate  the  capacitance  or  inductance  of  such  condensers  and  coils 
as  are  commonly  employed.  The  most  important  design  formula  is  the  one  for 
wave  length, 

\m=1884.i/CL 

where  C  is  in  microfarads  and  L  in  microhenries  and  A  in  meters. 


RADIO    COMMUNICATION. 


279 


Trans-Tiitting  Condensers.— The  amount  of  capacitance  needed  in  the  condenser 
in  the  closed  transmitting  circuit  may  be  determined  from  the  formula 


(87) 


NE0* 


where  C is  the  capacitance  in  mfd.,  P  is  the  power  in  watts,  Nis  the  number  of  con- 
denser charges  per  second,  and  E0  is  the  maximum  emf.  in  volts.  It  may  be  seen 
from  this  that  if  a  low  voltage  E0  is  used,  the  capacitance  needed  for  a  given  power 
will  be  large  and  if  a  high  voltage  is  used  the  capacitance  may  be  smaller.  Thero  is 
a  large  reduction  of  capacitance  with  a  small  increase  of  voltage  because  the  voltage 
term  is  squared,  therefore  to  avoid  using  unduly  large  condensers  it  is  well  to  USD 


Fia.  207 


-5«el"iorvsJ  view 
Wound  <jf  m«t»[  ribborv 


Side,    view    rff  f  Ut  »f>l'r*l 


as  high  a  voltage  as  possible  without  brush  discharge  taking  place.  For  instance, 
if  the  voltage  were  doubled,  a  condenser  only  one  fourth  as  large  could  be  used  for 
the  same  power.  As  an  illustration,  if  it  is  desired  to  use  \  kw.  at  12,000  volts,  with 
1000  sparks  per  second, 

0.007mfd. 


1000  X  144  X106 

Knowing  the  total  capacitance  required,  the  number  of  sheets  of  dielectric  required 
to  make  up  the  condenser  is  obtained  from  the  formula, 


(88) 


280 


RADIO    COMMUNICATION. 


where  Kis  the  dielectric  constant,  n  is  the  number  of  sheets  of  dielectric,  S  is  the  area 
in  cm.2  and  T  the  thickness  in  cm.  Supposing  that  mica  is  not  available,  it  may  be 
required  to  find  the  number  of  sheets  of  glass  required  to  make  up  the  condenser 
of  0.007  mfd.  required  above.  Suppose  the  sheets  are  15  by  20  cm.,  0.25  cm.  thick, 
and  the  dielectric  constant  is  7.  Substituting  in  the  formula  just  given, 

0. 25X0.007X10'* 
W~0.0885X  7X15X20 

Thus  nine  sheets  of  this  dielectric  are  needed. 

It  should  be  noted  that  the  higher  the  spark  frequency  JV,  the  smaller  may  be  the 
condenser  used  to  give  the  same  power.  For  this  reason,  as  well  as  the  others  previ- 
ously given,  it  is  a  distinct  advantage  to  use  a  high  spark  frequency. 

When  the  voltage  at  which  it  is  desired  to  operate  the  spark  gap  is  so  high  that  it 
will  break  down  the  particular  insulation  used  in  the  condensers,  or  cause  brush 
discharge,  the  connection  of  four  condensers  each  of  capacitance  C,  as  shown  in  Tig. 
206,  p.  276,  will  give  a  resultant  capacitance  C,  while  subjecting  each  condenser  to 
only  half  the  full  voltage. 

Inductance  Coils. — The  principal  inductance  coils  in  a  radio  set  are  the  primary 
and  secondary  of  the  oscillation  transformer  and  the  antenna  loading  coil,  and  tl.e 


Ficj.211 


^J  F,<s.  2/2 


.  213 


oss  5ection  of  "Tingle  layer  coif 


three  corresponding  coils  of  the  receiving  set.  The  three  coils , oscillation  primary, 
and  secondary,  and  loading  coil,  are  very  similar.  In  actual  practice  few  operators 
know  even  approximate  values  of  the  inductances;  a  standard  form  is  used,  depend- 
ing somewhat  on  the  size  of  the  set,  and  adjustments  by  clips  or  taps  enable  the 
proper  values  to  be  used.  In  order  to  design  a  set,  the  inductances  of  the  coils  are 
calculated  and  an  allowance  made  for  the  small  inductance  in  the  leads  and  other 
parts  of  the  circuit.  The  form  usually  used  for  coils  in  transmitting  circuits  are 
either  the  helix  (single  layer  spaced  coil)  of  round  wire,  or  edgewise  wound  strip, 
Figs.  207  and  208,  or  the  flat  spiral  or  pancake  of  bare  metal  ribbon,  Figs.  209  and 
210.  For  wavemeters  a  multi-layer  coil  is  used  having  wires  insulated  and  close 
together,  Figs.  211  and  212.  For  receiving  coils  the  common  form  is  a  single  layer 
of  insulated  wires,  Fig.  213.  The  coils  are  supported  or  held  together  by  some  insulat- 
ing material,  and  no  iron  is  used  in  them. 


RADIO    COMMUNICATION. 


281 


Hdii  of  Round  Wire.— The  inductance  of  the  coil  of  Fig.  205  is  given  in  micro- 
henries by 

L=0.039MW  (8Q) 

where  a  and  6  are  shown  in  Fig.  211,  a  being  the  mean  radius  of  the  solenoid  and  6 
the  total  length  of  the  solenoid;  n  is  the  number  of  turns  of  wire;  d  is  the  diameter 
of  the  bare  wire;  and  -fiTis  a  shape  factor  depending  upon  the  relative  dimensions, 
all  lengths  being  expressed  in  centimeters.  A  brief  table  of  values  of  K  is  given 
below.  In  the  figure,  D  is  the  pitch  of  the  winding  or  the  distance  between  centers 
of  adjacent  wires;  c  is  the  radial  thickness  of  the  winding. 

As  an  example,  find  the  inductance  of  a  solenoid  having  15  turns  of  bare  wire  of 
diameter  0.4  cm.,  pitch  of  winding  1.1  cm.,  diameter  of  core  24  cm.  In  the  formula 
d=QA  cm.,  Z>=1.1  cm.,  n=15,  b=«D=16.5  cm.,  a=12+.2=12.2  cm.  Then  with 

^=rL--=1.48,  K  is  found  as  0.598.  From  the  above  formula  the  inductance  in  micro- 
0  16.5 

henries  is  given  by 


16.5 

If  it  is  desired  to  compute  the  inductance  more  closely  than  a  few  per  cent,  more 
accurate  formulae  should  be  used  as  given  in  C.  74,  p.  253. 
TABLE  OF  VALUES  OF  K. 
(Shape  Factor  of  Helical  Inductance  Coils.) 


Diameter 

Diameter 

Diameter 

Length 

Length 

Length 

0.00 

1.000 

0.70 

0.761 

3.50 

0.394 

.C5 

0.979 

0.80 

.735 

4.00 

.365 

.10 

.959 

O.CO 

.711 

5.0 

.320 

.15 

.939 

1.00 

.688 

6.0 

.285 

.20 

.920 

1.25 

.638 

7.0 

.258 

.25 

.902 

1.50 

.595 

8.0 

.237 

.30 

.884 

1..75 

.558 

9.0 

.219 

.<10 

.850 

2.00 

.526 

10.0 

.203 

.£0 

.818 

2.50 

.472 

25.0 

.105 

.CO 

.789 

3.00 

.429 

100.0 

.035 

Helix  of  Edgewise  Wound  Strip. — Refer  to  Fig.  208.    For  this  case  the  formula  is 
,     0. 0395  aWK       0. 0126  ti*ac 


(90) 


microhenries,  where  K  is  given  in  the  table  above. 

As  an  illustration  of  use  of  the  formula,  a  helix  of  30  turns  is  wound  with  metal 
strip  0.635  cm.  wide  by  0.159  cm.  thick  with  a  winding  pitch  of  0.635  cm.,  to  form  a 
solenoid  of  mean  diameter  25.4  cm.  Here  J>=0.635  cm.,  o=12.7  cm.,  c=0.635  cm., 

6=nZ>= 30X0.635=  19.05  cm.    For  y=1.333,  ^=0.623. 
Then  from  the  above  formula 


0. 0395X12. 72X900X0. 623     0. 0126X900X12.  7X0. 635 


19.05 
£=187.4—4.0 
L= 182.5  microhenries. 


19.05 


282 


RADIO    COMMUNICATION. 


Flat  Spiral.—  See  Figs.  209  and  210.    The  inductance,  is  given  by 
i=0.01257  ^2x2.303l+-+-log1o-yi+-    , 


(91) 


where  a=ai+i  (n-\~)D;  d=  -b2+c2;  and  y\  and  y3  are  shape  f.ictors  {riven  in  the  follow. 
ing  table.    See  example  below. 

Shape  Factors  for  Flat  Spiral  Inductance. 


b/c 

yi 

73 

b/c 

yi 

ys 

0 

0.500 

0.597 

0.50 

0.796 

0.677 

0.025 

.525 

.598 

.55 

808 

6CO 

05 

.549 

.599 

.00 

818 

702 

10 

.592 

.602 

.65 

826 

715 

15 

.631 

.608 

.70 

833 

729 

20 

.685 

.615 

.75 

838 

742 

25 

.695 

.624 

.80 

842 

7C6 

CO 

.722 

.633 

.85 

845 

771 

C/J 

.745 

.643 

.90 

847 

7C6 

40 

.704 

.654 

.95 

848 

801 

45 

.782 

.665 

1.00 

848 

816 

Illustration.— A  flat  spiral  of  38  turns  is  wound  with  copper  ribbon  whose  cross 
sectional  dimensions  are  0.953  cm.  (3/8  in.)  by  0.795  cm.  (1/32  in.),  the  inner  diameter 
being  10.3  cm.,  and  the  measured  pitch  0.4  cm.  Here  «=38, &=0.9c3,  D=0.4,  c=nD= 

38X0.4=15.2  cm.;  2ai=10.3  therefore  a=5.15+  0  X0.4=12.55  cm.;  d=  Vo.9532+15.22= 


6.592;  ~  =0-0002; 


=0.0152;  ~  =0.091;  &/c=0.0627. 


Then   from 


15.23  cm.; 

U  .»_-'/ 

the  table,  3/1=0.5604  and  j/3=0.599.    From  the  above  formula, 

i=0.01257X12.55X382X[2.303X1.015Xlogio6.592-0.5604+0.031X0.59G] 
i=323.3  microhenries. 

This  is  correct  to  $  of  1  per  cent. 

Multi-Layer  Coil.— The  coil  is  made  of  insulated  wire  closely  wound  as  in  Fig.  211. 

Such  coils  are  used  in  wavemeters.    The  insulating  frame  on  which  the  coil  is  wound 

has  the  cross  section  shown  in  Fig.  212.    The  inductance  is  given  by 


where  .Eis  given  by  the  following  table: 


b/c 

E 

b/c 

E 

1 

0.000 

12 

0.289 

2 

.120 

14 

.296 

3 

.175 

16 

.302 

4 

.208 

18 

.3C6 

5 

.229 

20 

.310 

6 

.245 

22 

.313 

7 

.256 

24 

.316 

8 

.266 

26 

.318 

9 

.273 

28 

.320 

10 

.279 

30 

.322 

RADIO    COMMUNICATION. 


283 


As  an  illustration,  a  coil  has  15  layers  of  insulated  wire,  with  15  turns  to  a  layer 
the  mean  radius  being  5  cm.  The  coil  is  1.5  cm.  deep  and  1.5  cm.  in  axial  length. 
Here  o=5,  n=225,  6=c=1.5.  From  the  tables  K  is  0.267  and  E  is  zero.  Then  the 
formula  gives 

0:03948X25X2252x()  ^^  o.01257X^_X5X  1.5^  ^ 

1.5  1.5 

L=  8887-  2205 
i=6682  microhenries. 

Single  Layer  Coil.—  Refer  to  Fig.  213.  The  inductance  is  computed  by  the  formula 
(89).  As  an  illustration,  a  coil  has  400  turns  of  wire  in  a  single  layer,  pitch  of  winding 
0.1  cm.,  radius  of  coil  out  to  center  of  wire  10cm.  Here  a=  10,  w=400,  Z>=0.1,  b=nD 


=40.    With^-g-0.5 

_     0.03948X100X4002 
J[/= 77: 


is  found  as  °-818- 


X 0.818=  1290  microhenries. 


For  any  other  inductance  calculations  see  C.  74,  Sections  66  to  73. 

171.  Simple  Field  Measurements. — On  high  power  radio  trans- 
mitting sets  it  is  desirable  to  have  instruments  reading  the  current 
taken  from  the  generator,  the  voltage  of  the  same,  the  power  so 
taken  and  the  frequency  of  the  current.  The  four  instruments, 
ammeter,  voltmeter,  wattmeter  and  frequency  meter,  are  perma- 
nently mounted  on  the  switchboard.  The  measurements  of  the 
various  radio  quantities  are  explained  below. 

Voltage. — A  simple  method  of  measuring  a  voltage,  either  at  radio 
or  low  frequencies  is  to  measure  the  distance  a  spark  jumps  between 
electrodes  of  a  given  shape  and  size  in  air.  Following  is  a  table 
showing  approximately  the  "spark  voltages"  in  air  between  brass 
balls  2  cm.  in  diameter  for  various  spark  lengths. 


Spark 
Length  in 

Spark  Voltage. 

Cm. 

0.1 

4,700 

0.2 

8,100 

0.3 

11,400 

0.4 

14,  £00 

0.5 

17,500 

O.G 

20,400 

1.0 

31,300 

2.0 

47,  400 

Current. — The  principal  current  measurement  in  practice  is  that 
of  the  current  in  the  antenna.  A  hot  wire  ammeter  is  inserted  in  the 
lead-in  or  ground  wire.  If  its  reading  is  lower  than  normal,  it  indi- 
cates trouble  in  the  adjustment  of  the  apparatus,  or  in  the  grounding, 


284  RADIO    COMMUNICATION. 

and  means  decreased  distance  of  transmission.  In  order  to  avoid 
undue  interference  with  other  stations,  the  ammeter  current  should 
be  kept  as  small  as  will  give  the  needed  range.  As  has  been  stated 
before,  a  low  resistance  lamp  can  be  used  in  place  of  the  ammeter. 
When  the  closed  circuit  and  antenna  are  not  in  resonance,  the  lamp 
burns  feebly  or  not  at  all.  Current  measurements  are  also  necessary 
in  connection  with  some  of  the  various  measurements. 

Wave  Lengths. — The  theory  and  use  of  the  wavemeter  have  been 
discussed  in  Sections  112  and  168.  A  wavemeter  placed  in  inductive 
coupling  with  a  coil  or  antenna  carrying  radio  current  will  show  pro- 
nounced increase  of  current  in  its  own  coil  and  condenser  when  it  is 
tuned  to  resonance  with  the  source.  The  wave  length  is  read 
directly  from  the  wavemeter  setting  for  resonance,  or  from  a  calibra- 
tion curve.  A  receiving  set  can  be  used  to  measure  the  wave  lengths 
of  received  waves  if  it  is  first  standardized  in  terms  of  wave  lengths. 
This  standardization  is  done  by  the  arrangement  of  apparatus  shown 
in  Fig.  214,  where  Z  is  a  buzzer,  LC  a  wavemeter,  and  A  the  induc- 
tance coil  of  the  receiving  circuit. 

The  operator  listens  in  the  telephone  of  the  receiving  set,  (not 
shown  in  the  figure).  As  the  wavemeter  condenser  knob  is  turned 
the  loudest  sound  is  heard  when  the  wavemeter  circuit  is  tuned  to 
the  same  wave  length  as  that  for  which  the  receiving  set  is  adjusted. 
The  wave  length  is  then  read  from  the  wavemeter  scale  or  calibration 
curve.  Continuing  in  this  manner,  the  receiving  circuit  can  be 
calibrated  as  a  wavemeter,  by  setting  it  at  many  different  adjust- 
ments and  reading  the  wave  lengths  at  resonance  each  time.  The 
wavemeter  need  never  be  used,  after  that,  for  received  waves,  and 
the  operator  always  knows  where  to  tune  for  any  wave  length. 

Inductance. — To  find  the  unknown  inductance  Lx  of  a  coil,  a 
tuned  source,  which  need  not  be  a  wavemeter,  is  excited  by  a  buzzer, 
shown  at  Z  in  Fig.  215-A.  A  wavemeter  with  a  coil  of  known  induc- 
tance L  is  brought  near  and  its  variable  condenser  C  adjusted  to 
resonance  by  means  of  a  detector  and  telephone.  L  is  then  replaced 
by  Lx  and  a  new  value  of  capacitance  Ct  is  found  for  resonance. 

Then  L  C=LX  Cl  and  Lx  is  found  as  L  -~-,  or  as  L  (  —  j  if  the  waveme- 
ter reads  directly  in  wave  lengths.  The  value  thus  measured  is  the 
apparent  inductance  which  depends  somewhat  on  the  frequency  of 
oscillation.  (See  Section  114.)  Values  of  Lx  can  be  obtained  at 
different  frequencies  of  the  source. 


2  1  Tiq.  Z14 


Wave  Length  Calibration 
of  a  Receiving  Set. 


Titj.  215-A 


rdH'l- 


S-* 

d 

s? 

*                   S 

o  5 

7*\ 

— 

0  ^ 

4 

0  * 

F/j.  ZI5--B 


0 
0 


fly.  2/6 -A 


o 

0 


Tiq.  ZI6-B 


i(.  217 


285 


286  RADIO    COMMUNICATION. 

A  second  way  is  by  the  use  of  a  standard  condenser  instead  of  a 
standard  coil;  (See  Fig.  215-B).  Lx  is  connected  to  the  standard 
condenser  C  and  that  circuit  is  set  in  oscillation  by  the  buzzer  Z. 
The  wave  length  is  measured  by  a  wavemeter,  and  Lx  is  computed 

from  XTO=1884  VCl^. 

Capacitance  of  condensers. — The  simplest  method  is  that  of  com- 
parison with  a  standard  variable  condenser.  A  tuned  circuit  LC 
is  excited  by  a  buzzer,  Z  in  Fig.  216-A.  The  unknown  condenser  Cx 
is  placed  in  series  with  an  inductance  coil  L}  and  the  buzzer  circuit 
adjusted  to  resonance,  using  the  detector  and  telephone  of  the 
circuit  under  test.  The  unknown  condenser  Cx  is  then  replaced  by 
the  standard  condenser  Cs  which  is  now  adjusted  to  resonance  with 
the  buzzer  circuit.  The  capacitance  of  the  unknown  condenser 
is  then  the  same  as  that  read  on  the  standard. 

If  a  standard  condenser  is  not  obtainable,  the  capacitance  of  the 
unknown  variable  condenser  can  be  found  by  connecting  it  to  an 
inductance  of  known  value  L  and  exciting  the  circuit  by  a  buzzer. 
The  wave  length  is  read  on  a  wavemeter  (Fig.  216-B).  Cx  is  found 
from  Xm  =  1884V  CXL. 

Accurate  results  are  easily  obtained  by  the  first  method  described, 
that  of  comparison;  but  the  second  method  is  open  to  error  because 
of  the  distributed  capacitance  of  the  lead  wires  and  the  coil,  and 
the  inductance  of  the  leads.  The  effect  is  slight  if  the  capacitances 
employed  are  large. 

Resistance  and  Decrement. — Three  simple  methods  are  available 
for  measurement  of  high  frequency  resistance  or  decrement,  (1)  resist- 
ance substitution,  (2)  resistance  variation,  and  (3)  reactance  varia. 
tion.  After  the  resistance  R  is  known,  a  simple  relation  5=19.7  RfC 
enables  the  decrement  to  be  computed,  or  vice  versa.  C  is  the 
capacitance  at  resonance  and  is  known  from  the  condenser  setting. 
Of  the  three  methods,  the  first  is  the  best  if  a  variable  high  frequency 
resistance  standard  is  available;  the  second  is  a  good  all  round 
method,  requiring  resistance  standards,  but  these  need  not  be  varia- 
ble; the  third  requires  no  resistance  standard,  and  is  especially 
suited  to  measuring  the  decrement  of  a  wave.  In  all  three  methods, 
the  best  results  are  obtained  if  the  exciting  source  gives  continuous 
or  only  slightly  damped  current.  In  the  resistance  substitution 
method,  the  resistance  R  to  be  measured  is  inserted  in  a  tuned 
circuit  with  a  variable  condenser  C  and  inductance  coil  L  coupled 
loosely  to  the  source,  as  shown  in  Fig.  217.  A  hot  wire  ammeter  is 


RADIO    COMMUNICATION.  287 

inserted  at  A.  The  circuit  is  tuned  to  the  source  and  the  reading 
of  A  noted.  The  resistance  R  is  then  replaced  by  a  variable  resist- 
ance standard  which  is  adjusted  until  the  ammeter  reading  is  the 
same  as  it  was  before.  The  known  amount  of  resistance  inserted 
is  the  same  as  R.  Resistance  standards  for  radio  work  must  be  of 
line  wire  to  avoid  skin  effect,  and  must  be  short  and  straight  in  order 
to  have  very  little  inductance.  For  additional  information  on 
measurements  see  Circular  74. 

B.  Apparatus  for  Undamped  Wave  Transmission. 

172.  Advantages  of  Undamped  Oscillations. — Undamped  oscilla- 
tions are   not  broken   up   into  groups   like   damped   oscillations. 
Exactly  similar  current  cycles  follow  one  another  continuously, 
except  as  they  are  interrupted  by  the  sending  key,  or  subjected  to 
gradual  fluctuations  of  intensity  as  when  used  for  radio  telephony. 
Undamped  oscillations  are  produced  by  a  high  frequency  alternator, 
an  arc,  or  vacuum  tubes.     This  chapter  does  not  take  up  vacuum 
tubes  and  their  uses,   these  being  treated  in  the  following  chap- 
ter.    The  main  advantages  of  undamped  waves  are  the  following: 
(1)  Radio  telephony  is  made  possible.     (2)  Extremely  sharp  tuning 
is  obtained  and  consequent  reduction  of  interference  between  sta- 
tions working  close  together.     A  slight  change  of  adjustment  throws 
a  receiving  set  out  of  tune,  and  the  operator  may  pass  over  the  cor- 
rect tuning  point  by  too  rapid  a  movement  of  the  adjusting  knobs. 

(3)  Since  the  oscillations  go  on  continuously  instead  of  only  a  small 
fraction  of  the  time,  as  in  the  case  of  damped  waves,  (Section  160) 
their  amplitudes  need  not  be  so  great,  and  hence  the  voltages 
applied  to  the  transmitting  condenser  and  antenna  are  much  lower. 

(4)  With  damped  waves  the  pitch  or  tone  of  received  signals  de- 
pends wholly  upon  the  number  of  sparks  per  second  at  the  trans- 
mitter.    With  undamped  waves  the  receiving  operator  controls  the 
tone  of  the  received  signals,  and  this  can  be  varied  and  made  as 
high  as  desired  to  distinguish  it  from  strays,  and  to  suit  the  sensi- 
tiveness of  the  ear  and  the  telephone.     These  advantages,  freedom 
from  interference  from  other  stations  through  selective  tuning,  the 
use  of  high  tones  and  low  voltages,  and  the  greater  freedom  from 
strays  combine  to  permit  a  higher  speed  of  telegraphy  than  could 
otherwise  be  obtained. 

173.  Use  of  High  Frequency  Alternators. — For  the  production  of 
continuous  oscillations  an  alternating  current  generator  of  very  high 


288 


RADIO    COMMUNICATION. 


frequency  can  be  used.  See  Section  95.  This  is  connected  directly 
or  inductively  to  the  antenna  and  ground.  See  Fig.  218.  This 
constitutes  the  simplest  possible  connection  for  producing  continu- 
ous waves.  However,  to  obtain  a  wave  length  as  short  as  1500 
meters,  the  frequency  of  the  alternating  current  must  be  as  high  as 
200,000  cycles  per  second.  The  generator  speed  required  to  pro- 
duce this  frequency  is  so  high  that  a  special  type  of  construction  is 
needed  for  such  a  machine.  It  is  also  necessary  to  have  apparatus 
for  keeping  the  speed  constant,  so  that  the  wave  length  will  not 
change  ( since /Xm=300,000,000).  This  method  is  not  available  for 


Fia.  l\<\ 


Fia  218 

J 


Continuous    oseilLfi'ons  from  ol.  e  -  Are. 


CorrenT 

Current  voltage  character  lafric 
of  the  Arc. 


corvh'nuoua  wavaa 


generating  very  short  waves;  for  these,  the  oscillating  vacuum  tube 
is  used.     See  Section  198. 

174.  Arc  Sets.— A  much  used  method  for  producing  undamped 
waves  of  rather  great  wave  length  is  by  means  of  a  d.c.  arc  operated 
on  about  500  volts.  It  has  been  discovered  that  an  electric  arc 
between  proper  electrodes  shunted  by  an  inductance  coil  and  a 
condenser  will  produce  undamped  oscillations  through  the  shunt 
circuit.  The  connection  is  shown  in  Fig.  219.  The  operation  is  as 
follows. 


RADIO    COMMUNICATION.  289 

The  current  through  the  arc  is  always  in  the  same  direction  but 
may  vary  in  magnitude.  It  is  found  that  when  the  current  in  the 
arc  increases,  the  voltage  at  its  terminals  falls  off  (see  Fig.  220). 
Suppose  the  arc  to  be  burning  steadily  with  the  CL  circuit  discon- 
nected. If  now  the  circuit  is  connected,  the  condenser  C  begins 
charging  with  the  left  plate  in  Fig.  219  positive,  and  draws  current 
away  from  the  arc.  The  potential  difference  of  the  arc  increases 
(Fig.  220)  and  helps  the  charging.  The  charging  continues  until 
the  counter  emf.  of  the  condenser  equals  that  applied.  As  the 
charging  nears  its  end,  the  charging  current  becomes  gradually  less, 
and  the  arc  current  as  a  whole  increases  to  its  normal  value,  with  a 
corresponding  drop  in  voltage.  The  condenser  then  begins  to  dis- 
charge downward  through  the  arc,  increasing  the  arc  current,  and 
lowering  its  voltage.  Lowering  the  voltage  across  the  terminals  of 
the  arc  aids  the  condenser  to  discharge,  and  the  effect  of  the  induc- 
tance in  the  circuit  tends  to  keep  the  current  flowing,  and  a  charge 
is  accumulated  on  the  condenser  plates  of  the  opposite  sign  from  the 
first  one.  As  the  charge  now  nears  its  end,  the  charging  current 
downward  through  the  arc  becomes  gradually  less,  and  the  arc 
current  decreases,  causing  the  voltage  to  rise.  From  Fig.  219  it  is 
seen  that  the  rise  of  d.c.  voltage  is  such  as  to  attempt  to  charge  the 
left  plate  of  C  positive,  and  the  positive  charges  on  the  right  hand 
plate  begin  at  once  to  come  back,  going  up  through  the  arc  and 
decreasing  the  current.  There  is  a  consequent  further  rise  of  vol- 
tage (Fig.  220),  and  in  a  direction  to  assist  first  the  condenser  dis- 
charge, and  then  the  recharge  in  the  opposite  direction  (on  the  left 
hand  plate).  The  action  now  begins  all  over  again,  and  thus  con- 
tinuous oscillations  take  place  through  the  circuit. 

Use  is  made  of  this  phenomenon  by  coupling  the  coil  L  to  the 
antenna,  as  in  Fig.  221,  where  the  schematic  diagram  of  a  complete 
arc  transmitting  set  is  shown.  The  d.c.  generator  is  shown  with 
choke  coils  KK  to  prevent  the  high  frequency  oscillations  from  get- 
ting back  into  the  generator.  B  is  a  ballast  resistance.  A  larger  oscil- 
lating current  is  produced  if  the  arc  is  burned  in  a  strong  magnetic 
field,  producing  a  quenching  action  on  the  arc,  and  for  that  purpose 
the  magnets  MM  sue  provided.  Also  the  arc  burns  in  a  closed  cham- 
ber having  hydrogen  passing  through.  The  positive  electrode  is 
copper  and  the  negative  solid  carbon,  both  being  of  large  size  and 
cooled  by  a  water  jacket.  The  shunt  circuit  CL  is  the  same  as  in 
Fig.  219.  The  key  is  arranged  to  short  circuit  some  of  the  turns  of 
97340°— 19 19 


290  RADIO    COMMUNICATION. 

inductance  in  the  antenna  circuit,  the  correct  number  of  turns 
being  adjusted  for  resonance  with  the  key  closed.  Then  with  the 
key  open,  the  antenna  circuit  is  out  of  tune  with  the  arc  oscillations 
and  the  current  is  negligible,  thus  forming  the  intervals  between 
dots  and  dashes. 

A  simple  modification  of  Fig.  218  or  Fig.  221  will  enable  the  appa- 
ratus to  be  used  for  radio  telephone  transmission.  One  method  is 
to  insert  in  the  ground  wire  a  telephone  transmitter  capable  of  carry- 
Ing  the  antenna  current.  The  vibrations  within  the  transmitter 
-caused  by  sound  waves  alter  the  resistance  and  modify  the  radio 
-oscillations  and  transmitted  waves.1 

175.  Calibration  and  Adjustment  of  Sets. — With  a  high  frequency 
alternator  the  frequency  and  hence  the  wave  length  are  determined 
by  the  speed  of  the  generator  and  the  number  of  poles.     The  induc- 
tance and  capacitance  of  the  antenna  should  be  of  such  values  as  to 
give  the  circuit  the  same  natural  frequency  as  the  generated  current. 
This  is  brought  about  by  adjusting  the  antenna  loading  coil  to  give 
maximum  current  in  the  hot  wire  ammeter  (Fig.  218). 

Much  the  same  method  is  used  with  arc  sets.  The  desired  wave 
length  is  obtained  by  adjustment  of  C  or  L  in  Figs.  219  and  221,  the 
antenna  circuit  being  opened,  and  the  wave  length  being  set  on  a 
wavemeter  which  is  brought  near.  The  antenna  circuit  is  then 
adjusted  to  the  same  wave  length  by  varying  the  loading  coil  until 
the  hot  wire  ammeter  gives  a  maximum  reading.  A  pilot  lamp  can 
be  used  instead  of  the  ammeter,  since  it  can  be  adjusted  by  a  shunt 
to  light  only  when  the  circuits  are  in  resonance.  Sometimes  this 
lamp  is  connected  inductively  by  a  loop  of  wire  instead  of  being 
directly  in  the  ground  wire. 

C.  Apparatus  for  Reception  of  Waves. 

176.  General  Principles. — Receiving  sets  are  divided  into  two 
general  classes,  those  for  damped  waves,  and  those  for  undamped 
waves.    Sets  for  damped  waves  in  practice  involve  the  simpler  con- 
nections and  form  a  good  starting  point  for  the  discussion,  although 
it  will  be  shown  later  in  introducing  undamped  wave  sets,  that  a 

1  In  Chapter  6,  Sections  202  to  204  this  action  is  explained,  and  improved  methods 
are  given  for  carrying  on  radio  telephony  by  means  of  vacuum  tubes.  For  discus- 
sion of  the  behavior  of  an  electric  arc,  and  its  application  to  radio  work,  the  reader 
is  referred  to  Fleming's  Principles  of  Electric  Wave  Telec^raphy  and  Telephony 
(3rd  edition),  pp.  95  to  115,  with  special  notice  of  pp.  Ill  and  112. 


RADIO    COMMUNICATION. 


291 


very  slight  modification  of  the  damped  wave  apparatus  will  give 
one  method  of  receiving  undamped  waves.  Damped  waves  are 
commonly  received  by  a  crystal  detector  or  a  vacuum  tube  detector 
(see  Sections  179  and  191)  and  a  telephone  receiver.  The  tone 
heard  in  the  telephone  is  that  of  the  groups  of  damped  waves. 
Undamped  waves  are  ordinarily  received  by  a  vacuum  tube  method 
which  produces  beats  (see  autodyne  method,  p.  336).  These  will  be 
made  clear  in  the  diagrams  which  follow,  where,  for  the  purpose  of 
explaining  principles,  the  simplest  possible  sets  will  be  shown  first, 
even  though  not  now  used  in  military  work. 

The  fundamental  principle  of  reception  of  signals  is  that  of  reso- 
nance.    If  the  receiving  circuits  are  tuned  to  oscillate  at  the  same 


FIG.  Ill 


213 


•for  reception  of 
radio  waves 


Action  of  rectifier  on  received 


224- 


"for  reception  eff 
radi  ' 


Fia.  225 

L3      <imH«  toned! 


reeeivirvjt 

*»arf«3 


natural  frequency  as  the  incoming  waves,  then  these  waves,  though 
extremely  feeble,  will  after  a  few  impulses,  build  up  comparatively 
big  oscillations  in  the  circuits.  In  reality,  then,  for  reception  of 
signals,  all  that  is  needed  is  an  antenna  circuit  tuned  to  the  same 
wave  lengths  as  that  of  the  transmitting  station,  and  an  instrument 
capable  of  evidencing  the  current  which  flows  in  the  antenna  con- 
necting wire.  This  is  shown  in  Fig.  222.  This  is  the  simplest  pos- 


292  RADIO    COMMUNICATION. 

sible  arrangement  for  reception,  and  will  operate  on  either  damped 
or  undamped  waves.  A.  current  indicating  instrument  is  shown  at  A . 
In  practice  the  current  is  too  feeble  for  any  hot  wire  ammeter.  An 
ammeter  is  more  suitable  for  quantitive  measurements  than  for 
receiving  telegraphic  signals,  since  the  dots  and  dashes  are  not 
readily  distinguished  unless  made  so  slowly  as  to  be  impracticable 
for  transmitting  messages. 

Use  of  the  Telephone. — A  more  sensitive  receiving  device  is  a  tele- 
phone receiver  having  a  large  number  of  turns  of  wire  compactly 
wound.  The  current  is  made  manifest  by  vibrations  of  the  dia- 
phragm at  audible  frequency,  but  the  frequency  of  a  radio  current 
is  so  high  that  the  diaphragm  cannot  possibly  follow  it.  The  effect 
is  as  if  the  diaphragm  tried  to  go  both  ways  at  once,  with  the  result 
that  no  observable  motion  takes  place.  To  remove  this  difficulty  a 
crystal  rectifier  is  put  into  the  circuit,  which  permits  current  to 
flow  in  one  direction,  but  not  in  the  other;  or  more  exactly,  the  cur- 
rent in  the  reverse  direction  is  negligibly  small  compared  with  the 
current  in  the  principal  direction.  See  Fig.  51.  Referring  to  the 
reception  of  damped  waves,  it  is  well  to  remember  that  the  waves  are 
in  widely  separated  groups.  The  action  of  a  cystal  rectifier  upon 
damped  oscillations  is  shown  in  Fig.  223;  the  lower  halves  of  the 
waves  are  drawn  dotted  to  indicate  the  portion  of  the  current  that 
is  cut  off  by  the  rectifier. 

It  is  found  that  the  cumulative  effect  of  one  group  or  train  of  waves, 
for  instance  that  due  to  one  condenser  discharge  at  the  transmitter, 
pulls  the  telephone  diaphragm  away  from  its  neutral  position. 
The  number  of  such  pulls  per  second  is  equal  to  the  number  of  wave 
trains  per  second.  With  a  300-meter  wave  having  1000  wave  trains 
per  second  the  radio  frequency  is  1,000,000  and  the  audio  frequency 
is  1000,  or  one  is  a  thousand  tunes  as  high  as  the  other.  The  upper 
limit  of  audio  frequency  for  the  human  ear  is  16,000  to  20,000  sound 
waves  per  second,  so  that  even  if  the  telephone  diaphragm  could, 
without  a  rectifier,  follow  the  radio  frequency,  the  ear  would  not 
hear  the  signals.  In  telegraphic  signaling,  either  a  dot  or  a  dash 
lasts  long  enough  to  contain  many  wave  groups,  and  in  the  telephone, 
where  the  pitch  corresponds  to  the  spark  frequency,  a  tone  is  heard 
during  the  length  of  the  dot  or  dash. 

Simple  Receiving  Sets. — In  Fig.  224  is  shown  the  simplest  con- 
nection for  reception  with  a  telephone  receiver.  It  is  suitable 
only  for  damped  waves.  At  D  is  shown  the  rectifier,  commonly 


RADIO    COMMUNICATION.  293 

called  a  " detector,"  although  it  detects  nothing ;  it  alters  the  waves 
so  that  the  telephone  can  detect  them.  The  apparatus  as  shown 
receives  best  from  a  transmitter  of  the  same,  or  nearly  the  same 
wave  length.  It  is  true  that  the  presence  of  the  detector  and  tele- 
phone introduces  high  resistance  in  the  antenna  circuit  and  thus 
renders  it  not  very  selective,  so  that  it  will  respond  to  a  wide  range 
of  wave  lengths.  Tuning  to  resonance  is  made  possible  if  a  tuning 
coil  is  introduced  such  as  L  in  Fig.  225,  to  vary  the  inductance  of 
the  circuit  and  hence  the  wave  length.  This  is  a  connection  exactly 
analogous  to  the  plain  antenna  of  Fig.  194,  with  the  spark  gap  (the 
point  where  the  energy  enters  the  antenna)  replaced  by  the  detector 
and  telephone  (the  point  where  the  used  energy  leaves  the  antenna). 

It  is  well  to  notice  how  simple  is  the  apparatus  actually  needed 
for  reception,  contrary  to  what  the  uninitiated  person  supposes. 
Three  pieces  of  apparatus,  telephone  receiver,  rectifier  and  tuning 
coil  will  receive  effectively  from  damped  wave  stations.  The 
main  disadvantage  of  the  connection  of  Fig.  225  is  in  not  being  able  to 
tune  out  stations  that  one  does  not  wish  to  hear.  Also  the  ampli- 
tude of  the  oscillations  is  much  diminished  by  the  high  resistance 
of  the  detector  and  telephone.  The  principal  resistance  is  that 
of  the  detector. 

The  apparatus  of  Fig.  225  gives  about  the  same  results  if  the 
telephone  is  in  shunt  with  the  detector  instead  of  in  series  with 
it.  In  this  case  the  explanation  of  the  action  is  as  follows.  Sup- 
pose that  the  current  flows  easily  upward  through  the  rectifier,  but 
not  downward.  During  a  group  of  incoming  waves,  the  antenna 
thus  receives  an  accumulated  positive  charge,  and  during  the 
intervals  between 'wave  groups  it  discharges  downward  through  the 
telephone.  It  cannot  send  current  downward  through  the  rectifier. 
Thus  pulsations  of  current  pass  through  the  telephone  with  suc- 
cessive wave  groups. 

177.  Typical  Circuits  for  Reception  of  Damped  Waves. — To  avoid 
the  difficulties  attendant  upon  the  presence  of  the  detector  in  the 
antenna  circuit,  it  is  customary  to  place  the  detector  in  a  separate 
circuit  coupled  to  the  antenna;  or  another  viewpoint  is  that  the 
detecting  instruments  are  placed  as  a  shunt  to  the  tuning  coil. 
For  instance  Fig.  226  is  an  improvement  and  requires  no  more 
apparatus  than  Fig.  225  except  that  the  tuning  coil  has  two  adjust- 
able connections  instead  of  one.  Oscillations  now  take  place 
freely  between  the  antenna  and  ground.  Two  telephone  receivers 
are  shown,  connected  in  series,  one  for  each  ear. 


294 


RADIO    COMMUNICATION. 


Direct  Coupled  Receiving  Set. — A  further  improvement,  as  regards 
selectivity,  is  shown  in  Fig.  227,  where  a  variable  condenser  Cz  has 
been  added.  This  is  called  the  direct  coupled  connection.  Let 
Ll  be  the  inductance  in  the  antenna  circuit,  C\  the  capacitance 
between  the  antenna  and  ground,  and  L2  and  C2  the  corresponding 
constants  of  the  closed  circuit,  shown  by  heavy  lines.  The  antenna 
circuit  is  called  the  primary,  since  the  energy  enters  the  set  there. 
The  circuit  containing  L2  and  C2  is  called  the  secondary  and  is 
the  closed  oscillating  circuit.  In  the  same  manner  in  which  the 
transmitting  antenna  circuit  is  a  good  radiator  of  power,  so  the 
receiving  antenna  circuit  is  a  good  absorber.  It  is  tuned  to  reso- 
nance with  the  incoming  waves  by  adjustment  of  L±.  The  power 
is  given  over  magnetically  to  the  secondary,  which  is  tuned  to 


Direct   coupled  receiving  Set 


resonance  by  adjustments  of  7,2  and  C2.  Comparatively  large 
oscillations  result  in  the  secondary,  producing  voltages  across  the 
condenser  which  are  detected  by  the  crystal  and  telephone,  and 
which  are  not  in  either  oscillating  circuit.  The  oscillations  are 
not  damped  thereby,  and  sharp  tuning  is  obtained. 

Attention  is  invited  to  the  analogy  of  Fig.  227  with  the  coupled 
transmitting  set  of  Fig.  200  in  Section  166.  The  open  absorber  of 
one  corresponds  to  the  open  radiator  of  the  other;  the  closed  oscil- 
lating circuits  correspond,  each  having  its  L  and  C;  shunted  around 
the  condenser  in  one  case  (Fig.  227)  is  the  apparatus  where  the  used 
energy  is  taken  out,  namely,  the  detector  and  telephone,  and  in 
the  other  case  the  apparatus  where  the  energy  is  put  in,  namely,  the 
power  transformer  with  its  generator. 


RADIO    COMMUNICATION. 


295 


Inductively  Coupled  Receiving  Set. — In  Fig.  228  is  shown  the  in- 
ductively coupled  receiving  set.  This  may  be  taken  as  the  standard 
upon  which  all  later  changes  are  based.  A  fixed  condenser  of  about 
0.005  mfd.  is  shunted  around  the  telephone  and  this  increases  the 
strength  of  the  signals.  Its  action  is  explained  as  follows.  Suppose 
the  principal  current  flows  downward  through  the  detector  and 
telephone.  While  this  current  flows,  the  fixed  condenser  is  charged 
with  top  plate  positive.  When  the  reversal  of  the  radio  oscillation 
comes,  the  current  through  Z>  and  T  ceases.  Then  the  condenser 
discharges  down  through  T  and  tends  to  maintain  the  current  till 
the  next  oscillation  downward  through  the  instruments.  In  this 


Ftq.221 


way  the  gaps  between  the  successive  pulsations  of  rectified  current 
are  filled  in,  and  the  cumulative  effect  of  a  wave  group  is  strength- 
ened. In  practice  the  telephone  cord,  containing  as  it  does  two  con- 
ductors separated  by  dielectric,  forms  a  condenser  which  in  some 
cases  is  sufficient  so  that  an  added  fixed  condenser  gives  no  improve- 
ment. 

The  connection  in  Fig.  228  is  similar  in  its  action  to  the  direct 
coupled  arrangement  of  Fig.  227.  In  either  case,  on  account  of  the 
coupling  between  the  primary  and  secondary  coils,  there  are  re- 
actions of  each  coil  upon  the  other,  with  consequent  double  oscilla- 
tions when  the  coils  are  near  together.  See  Section  163.  Sharp 


296  RADIO    COMMUNICATION. 

tuning  becomes  impossible.  It  is  found,  however,  that  if  the  re- 
sistance of  the  circuits  is  low,  extremely  sharp  tuning  is  obtained. 
The  antenna  is  tuned  to  the  incoming  waves  by  changes  of  the 
inductance  Lv.  Sometimes  if  very  sharp  primary  tuning  is  desired, 
a  variable  condenser  is  shunted  around  Z-t,  and  fine  adjustments  are 
made  therewith.  The  secondary  is  tuned  to  the  primary,  the  opera- 
tions of  tuning  being  done  alternately  until  the  telephone  gives  the 
best  response.  In  the  secondary  the  coarser  timing  is  done  by 
changes  of  the  inductance  L2,  and  the  fine  tuning  with  the  variable 
condenser  C2. 

Comparing  Figs.  195  and  228,  it  will  be  found  that  the  circuits  are 
the  same.  One  finds  in  both  places  the  antenna  circuit  (radiator  or 
absorber),  the  closed  oscillating  circuit,  the  coupling  coils,  and  the 
power  inserted  or  detected  in  shunt  connections  to  the  condenser. 
The  main  difference  of  apparatus  is  that  instead  of  a  high  voltage 
condenser  as  in  Fig.  195,  C2  is  a  small  variable  air  condenser,  and 
instead  of  spaced-turn  coils  of  large  wire,  the  coils  of  the  receiving 
apparatus  have  many  turns  of  insulated  wire  closely  wound. 

For  receiving  a  longer  wave  in  the  primary  circuit  than  is  possible 
by  using  all  of  the  inductance  L2  a  series  inductance  L3,  called  a 
loading  coil,  is  added.  See  Fig.  229.  Also,  a  variable  condenser 
may  be  connected  as  shown  at  C3  to  increase  the  wave  length  and 
afford  fine  tuning.  The  secondary  may  also  be  provided  with  an 
extra  inductance  in  series  with  L2  if  needed.  For  receiving  short 
waves  on  a  large  antenna,  series  condenser  C4  is  inserted  in  the  ground 
wire.  It  is  short  circuited  when  not  in  use. 

In  the  typical  set  of  Fig.  228,  a  crystal  rectifier  (Section  179) 
is  used  as  the  detector.  The  principal  disadvantage  of  this  type  of 
detector  is  that  it  can  not  be  depended  upon  to  stay  in  adjustment. 
A  good  deal  of  time  is  required  for  the  frequent  readjustments. 
Fig.  230  shows  exactly  the  same  connection,  but  with  the  crystal 
detector  replaced  by  a  Fleming  valve,  V.  This  is  a  glass  bulb 
containing  two  electrodes  and  having  the  air  exhausted.  One 
electrode  in  the  vacuum  is  a  lamp  filament  which  is  heated  by 
current  from  a  storage  battery  A.  The  other  electrode  is  a  metal 
plate.  The  heated  filament  gives  off  a  stream  of  electrons  (Section 
184)  toward  the  plate.  Current  from  incoming  electric  waves  can 
pass  through  the  vacuum  in  only  one  direction  determined  by  the 
electrons,  the  current  in  the  opposite  direction  being  suppressed. 


RADIO   COMMUNICATION. 


297 


In  this  way  the  tube  acts  as  a  rectifier.  It  is  very  stable  and  about 
as  sensitive  as  a  good  crystal. 

A  still  further  improvement  is  shown  in  Fig.  231,  using  a  vacuum 
tube  having  three  electrodes.  It  is  seen  here  that  the  circuits 
joined  to  the  filament  and  the  nearer  electrode  are  exactly  the  same 
as  in  Fig.  230.  The  telephone,  however,  is  in  a  circuit  with  a  bat- 
tery B,  and  the  signals  received  thereby  are  much  louder  than  in 
the  case  of  Fig.  230.  For  the  theory  of  action  of  the  three-electrode 
vacuum  tube  as  a  detector  see  the  next  chapter,  Section  191. 

Capatitively  Coupled  Receiving  Set. — A  method  of  coupling  receiv- 
ing apparatus  to  the  antenna  circuit  which  affords  compactness 


Fiq.  231 


Flemiri  valva  or  two  electrode 
vacuum  Tub«  circuit 


Thr 
r«sc«iv.r^  circuit 


tub« 


is  shown  in  Fig.  232.  By  fixing  the  primary  and  secondary  coils 
LI  and  Z2  permanently  at  right  angles  to  each  other,  inductive 
coupling  between  the  two  is  prevented.  Instead,  the  coupling 
between  the  two  circuits  is  effected  through  the  condensers  CC, 
which  are  referred  to  as  "coupling  condensers."  Such  an  arrange- 
ment is  called  "  electrostatic"  or  "capacitive"  coupling.  The 
condensers  are  arranged  so  that  by  turning  one  handle  both  are 
varied  together.  One  of  the  condensers,  C,  the  one  connected  to 
earth,  may  be  omitted,  but  better  results  are  usually  obtained  with 
two.  The  advantages  of  capacitive  coupling  are  as  follows.  (1)  The 
coils  are  of  compact  form.  They  are  wound  as  rings  with  rectangu- 


298 


RADIO    COMMUNICATION. 


lar  or  square  winding  section,  thus  giving  large  inductances  in 
small  space.  This  is  a  great  saving  of  room  compared  with  sets 
using  variable  inductive  coupling  where  the  coils  must  be  so  con- 
structed that  one  of  them  can  move  with  respect  to  the  other,  and 
where  they  are  usually  wound  on  long  tubes  in  order  to  get  suitable 
variation  of  coupling.  (2)  The  coils  are  fixed.  In  the  inductive 
type  they  must  sometimes  be  separated  many  centimeters  for  very 
loose  coupling.  (3)  The  coupling  is  quickly  and  easily  changed. 
Sets  for  Quick  Tuning.- — When  simplicity  of  timing  is  the  principal 
requirement,  and  it  is  desired  to  reduce  the  tuning  operations  to  a 


y 


232 


Tio.233 


or  «l«ctr<x»t»tic  coo^i'^, 


jh^ 


. 

fc 


minimum  number,  even  at  the  expense  of  a  certain  amount  of 
selectivity,  the  following  methods  are  used. 

In  Fig.  233  is  shown  a  modification  of  the  capacitive  connection 
of  Fig.  235;  in  practice  the  change  from  one  to  another  is  accom- 
plished by  one  switch.  The  secondary  is  removed,  and  the  tele- 
phone is  put  in  shunt  with  the  detector  instead  of  with  the  fixed 
condenser  FC.  If  a  medium  value  of  coupling  is  used  it  is  not 
usually  necessary  to  alter  it,  therefore  the  only  tuning  adjustment 
is  that  of  the  primary  inductance. 

Another  device  for  quick  tuning  is  shown  in  Fig.  234.  This 
employs  an  inductive  coupling.  The  primary  is  tuned  sharply  to 
the  incoming  waves,  while  the  secondary  is  untuned.  With  the 
connections  as  shown,  the  secondary  will  respond  in  practically  the 


RADIO   COMMUNICATION. 


299 


same  manner  to  a  wide  range  of  wave  lengths,  owing  to  the  high 
resistance  of  the  detector.  Then  the  only  adjustment  the  operator 
has  to  make  is  that  of  the  primary  inductance.  Sometimes  addi- 
tional provision  is  made  for  adjustment  of  the  coupling  by  separating 
the  coils;  this  gives  variation  in  the  sharpness  of  tuning  and  in  the 
signal  strength. 

" Standby"  Circuits. — These  are  also  called  "pick-up"  circuits. 
When  listening  for  possible  calls  from  a  number  of  stations  it  is 
convenient  to  have  apparatus  which  will  respond  to  a  wide  variety 
of  wave  lengths.  The  circuit  of  Fig.  233  will  do  this  to  a  limited 
extent  if  the  coupling  is  close.  This  is  also  true  of  Fig.  234.  Prob- 


TikKer    metfiod  -for 
r«.ce.|"vin^   continuous 


Deterdyne  method 
conti'nuouj  waves 


ably  the  most  broadly  tuned  cf  all  the  receiving  sets  is  the  plain 
aerial  connection  already  shown  in  Fig.  224  or  Fig.  225.  It  is, 
however,  too  broadly  tuned  to  be  used  if  many  stations  are  trans- 
mitting. 

A  fairly  good  pick-up  circuit  is  the  ordinary  inductive  set  of 
Fig.  228  when  used  with  a  tight  coupling.  The  decrement  is  then 
high,  and  the  tuning  broad.  A  switch  may  be  provided,  if  desired, 
to  put  the  receiving  instruments  over  into  the  antenna  circuit. 

178.  Circuits  for  the  Reception  of  Undamped  Waves. — While 
damped  waves  are  transmitted  as  detached  groups  or  trains,  un- 


300  RADIO    COMMUNICATION. 

damped  waves  are  usually  not  separated  into  groups.  Undamped 
waves,  even  if  rectified,  will  not  be  detected  in  a  telephone  receiver 
unless  the  waves  are  broken  up  into  groups  in  some  way.  This  is 
because  the  telephone  diaphragm  and  the  ear  cannot  respond  to  so 
high  a  frequency  as  that  of  the  radio  oscillations.  Hence  it  is 
necessary  to  interrupt  the  undamped  wave  dot  or  dash  into  many 
groups  by  rapid  interruptions  of  the  current.  It  is  arranged  in 
practice  to  have,  for  example,  1000  interruptions  a  second,  and  as 
long  as  a  signal  continues  a  note  of  pitch  1000  is  heard.  These 
interruptions  may  be  made  to  take  place  either  at  the  transmitter 
or  at  the  receiving  station.  A  method  for  producing  them  at  the 
transmitting  station  is  to  insert  a  rapidly  operating  circuit  breaker 
called  a  "chopper"  in  the  antenna  wire;  or  if  it  is  inconvenient  to 
l:reak  the  current,  the  chopper  may  be  used  to  short  circuit  some 
of  the  turns  of  the  antenna  inductance  coil  to  throw  the  circuits 
out  of  resonance  periodically.  This  divides  up  the  waves  into 
groups  to  which  the  receiving  telephone  can  respond.  A  rather 
more  convenient  method  is  to  have  the  chopping  done  at  the  receiv- 
ing station,  for  then  the  receiving  operator  can  control  the  pitch 
of  the  received  signals.  There  are  at  least  five  ways  of  modifying 
the  waves  at  a  receiving  station  to  obtain  an  audible  frequency: 
(1)  a  chopper  in  series  with  the  detector  and  telephone;  (2)  a  vari- 
able condenser  with  rapidly  rotating  plates;  (3)  a  "tikker"  used 
instead  of  a  detector;  (4)  a  "heterodyne"  in  a  separate  circuit; 
(5)  an  "autodyne"  or  vacuum  tube  device  arranged  so  that  the 
detecting  tube  also  produces  the  heterodyne  action.  The  last 
method  is  explained  in  Section  201. 

Chopper. — This  may  be  any  device  for  rapidly  making  and  break- 
ing the  current.  It  is  inserted  in  the  circuit  of  the  detector  and  tel- 
ephone as  in  the  ordinary  damped  wave  set  of  Fig.  228.  It  con- 
sists of  a  rotating  toothed  wheel  with  a  stationary  contact  touching 
the  successive  teeth  or  a  break  controlled  by  an  electrically  operated 
tuning  fork,  or  it  is  sometimes  a  light  high  speed  vibrator  similar  to 
that  of  an  electric  bell. 

Rotating  Plate  Condenser. — If  the  movable  plates  of  the  tuning 
condenser  C2  in  Fig.  228  are  rotated  rapidly  the  apparatus  will  be 
in  tune  once  for  each  revolution.  Each  of  these  revolutions  will 
produce  an  impulse  of  the  telephone  diaphragm.  The  speed  can  be 
adjusted  so  that  the  impulses  will  cause  sounds  while  waves  are 
being  received.  In  practice  it  is  found  best  to  keep  part  of  the  ca- 


RADIO    COMMUNICATION.  301 

pacitance  of  the  condenser  C2  constant,  and  vary  only  a  part  of  it. 
If  the  main  plates  were  rotated  the  apparatus  would  give  sounds  at 
only  a  small  sector  of  each  revolution,  near  the  resonance  adjust- 
ment. To  accomplish  a  more  prolonged  train  of  impulses  during 
one  revolution  the  adjustment  can  be  held  near  resonance  for  a  larger 
proportion  of  the  time  if  the  rotating  condenser  is  made  very  small, 
and  is  put  in  parallel  with  C2.  The  latter  does  not  then  rotate  ex- 
cept for  ordinary  hand  tuning.  The  capacitance  of  C2  plus  the  max- 
imum capacitance  of  the  rotating  condenser  is  adjusted  to  give  res- 
onance. The  circuit  is  not  far  from  this  condition  when  the  moving 
plates  are  farthest  apart,  so  that  the  signals  affect  the  receiver  during 
a  considerable  portion  of  the  revolution. 

Tikker. — See  Fig.  235.  The  tikker  is  usually  a  stationary  fine  wire 
of  steel  or  gold  with  its  end  running  in  the  groove  of  a  smooth,  rota- 
ting brass  wheel.  It  is  a  slipping  contact  device.  The  wire  does 
not  remain  in  perfect  contact  with  the  wheel,  but  owing  to  the  slight 
irregularities  there  are  variations  of  contact,  which  in  effect  keep 
making  and  breaking  the  circuit.  With  the  tikker  contact  open, 
suppose  the  secondary  inductance  and  condenser  C2  to  be  tuned  to 
resonance  with  the  incoming  waves.  If  now  the  tikker  is  closed 
when  C2  has  any  stated  value  of  charge,  some  of  the  charge  will  be 
given  to  the  condenser  C  and  furthermore  the  radio  oscillations  cease 
because  the  addition  of  C  throws  the  apparatus  out  of  tune.  When 
the  tikker  is  opened  the  condenser  C  discharges  through  the  tele- 
phone, and  in  the  meantime  the  secondary  oscillations  build  up 
again,  ready  to  give  a  charge  over  to  C  when  the  contact  is  closed. 
In  this  manner  the  current  impulses  through  the  telephone  are  of 
the  same  frequency  as  the  operation  of  the  tikker,  and  this  can  be 
controlled  by  the  speed  of  the  wheel.  The  capacitance  of  C  should 
be  about  Imfd.  No  separate  rectifier  is  needed.  The  tone  obtained 
is  not  musical,  since  C2  is  charged  to  different  potential  differences 
at  the  different  times  when  the  tikker  closes,  and  the  action  depends 
also  upon  somewhat  irregular  contact. 

Heterodyne. — In  this  method  an  apparatus  is  arranged  to  produce 
undamped  electric  oscillations  in  the  receiving  circuit,  of  nearly 
the  same  frequency  as  that  of  the  waves  which  are  being  received, 
and  their  combined  action  is  made  to  affect  the  receiving  telephone. 
Beats  are  produced  having  a  frequency  equal  to  the  difference  of  the 
frequencies  of  the  two  waves.  The  connections  are  shown  diagrama- 
tically  in  Fig.  236.  Any  source  of  undamped  or  slightly  damped 


302  RADIO    COMMUNICATION. 

oscillations  is  connected  at  A.  In  the  antenna  circuit  at  B  is  a 
single  turn  or  loop,  coupled  inductively  to  A.  The  antenna  circuit 
thus  gets  the  effect  of  the  oscillations  from  A  as  well  as  from  the 
incoming  waves.  Suppose  those  received  have  a  frequency  of 
100,000,  and  the  heterodyne  A  is  adjusted  to  give  a  frequency  of 
99,000.  As  long  as  both  act,  the  telephone  will  respond  to  a  pitch  of 
1000  vibrations  per  second,  which  is  of  course  audible.  When  the 
incoming  waves  cease  the  heterodyne  continues  to  act  alone  at 
99,000  cycles,  but  is  inaudible.  Therefore  signals  are  heard  only 
during  the  time  when  the  incoming  radio  waves  are  received. 

Receiving  from  a  Radio  Telephone  Transmitter. — While  a  radio 
telephone  transmitting  apparatus  operates  on  undamped  waves  it 
is  not  necessary,  or  indeed  permissible,  to  use  a  chopper,  tikker, 
or  heterodyne  at  the  receiving  station.  The  transmitted  waves  are 
modified  or  varied  in  intensity  by  the  spoken  sounds  and  these 
sounds  are  reproduced  in  the  telephone  of  the  ordinary  receiving 
set  such  as  is  used  for  damped  waves. 

179.  Crystal  Detectors. — A  very  simple  and  convenient  kind  of 
detector  is  obtained  by  the  contact  of  two  dissimilar  solid  sub- 
stances, properly  chosen.  The  number  of  substances  which  have 
been  found  suitable  for  use  in  such  detectors  is  large.  This  type  of 
detector  is  easily  portable,  but  requires  frequent  adjustment  and 
is  less  sensitive  than  a  vacuum  tube.  For  field  sets  where  a  com- 
pact and  easily  portable  form  of  detector  is  required,  the  crystal 
detector  is  very  convenient.  The  use  of  crystal  detectors  is  largely 
confined  to  such  work  now,  and  even  in  the  portable  military  sets  is 
rapidly  giving  way  to  the  vaccuum  tube  detector. 

Crystals. — Among  the  combinations  of  solid  substances  which 
have  been  used  as  contact  detectors  may  be  mentioned  silicon  with 
steel,  carbon  with  steel  and  tellurium  with  aluminum.  The  most 
important  contact  detectors,  however,  consist  of  crystals,  natural 
or  artificial  in  contact  with  a  metallic  point.  Examples  of  such 
minerals  are  galena,  iron  pyrites,  molybdenite,  bornite,  chal copy- 
rite,  carborundum,  silicon  and  zincite.  The  first  three  are  respec- 
tively lead  sulphide,  iron  sulphide  and  molybdenum  sulphide. 
Bornite  and  chalcopyrite  are  combinations  of  the  sulphides  of  cop- 
per and  iron.  Carborundum  is  silicon  carbide,  formed  in  the  electric 
furnace.  The  fused  metallic  silicon  commonly  used  is  also  an  elec- 
tric furnace  product.  Zincite  is  a  natural  red  oxide  of  zinc. 

Probably  the  three  most  widely  used  crystals  are  galena,  silicon 
and  iron  pyrites.  Sensitive  specimens  of  iron  pyrites  are  more 


RADIO    COMMUNICATION. 


303 


difficult  to  find  than  sensitive  galena,  but  they  usually  retain  their 
sensitiveness  for  a  longer  time  than  galena.  These  sensitive  pyrite 
detectors  are  often  sold  under  the  trade  name  of  "Ferron."  The 
detector  sold  under  the  name  of  "Perikon"  consists  of  a  bornite 
point  in  contact  with  a  mass  of  zincite.  Fig.  237  shows  a  silicon- 
antimony  detector;  other  detectors  have  this  same  general  appear- 
ance. 

Properties. — In  order  to  act  as  a  detector  for  radio  signals  a  crystal 
contact  should  either  (1)  allow  more  current  to  flow  when  a  given 
voltage  is  applied  in  one  direction  than  when  it  is  applied  in  the 


FIG.  237.  —One  method  of  mounting  crystal  detectors. 

opposite  direction,  or  (2)  its  conductivity  should  vary  as  different 
voltages  in  the  same  direction  are  applied.  Practically  all  detec- 
tors formed  by  the  contact  of  two  dissimilar  substances  possess  both 
of  these  properties,  at  least  to  a  slight  extent. 

To  make  use  of  the  latter  property,  a  battery  is  required  in  series 
with  the  crystal,  as  explained  below.  Some  crystals,  such  as  galena, 
silicon  and  iron  pyrites  give  about  as  good  results  as  simple  recti- 
fiers as  when  the  battery  method  is  used.  They  are  ordinarily  used 
without  the  battery,  to  simplify  the  apparatus. 


304 


RADIO    COMMUNICATION. 


Fig.  238  shows  a  current- voltage  characteristic  curve  for  carborun- 
dum in  contact  with  a  metal.  The  current  flows  much  more  readily 
in  one  direction  than  in  the  other  under  equal  but  opposite  emfs. 
For  example,  under  a  constant  impressed  emf .  of  10  volts  in  one  di- 
rection a  current  of  100  microamp.  is  obtained,  while  with  the 
voltage  reversed  the  current  is  only  1  microamp.  This  illustrates 
the  property  of  ' '  unilateral  conductivity, ' '  or  rectification .  Further- 
more, as  regards  the  second  property,  when  the  voltage  is  applied  in 
the  direction  giving  the  larger  current,  the  conductivity  (ratio  of 


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current  to  voltage)  increases  as  the  voltage  increases.  This  is  shown 
by  the  right  hand  portion  of  the  figure.  The  characteristic  curve 
of  any  ordinary  metallic  conductor  would  be  a  straight  line. 

Booster  Battery. — In  order  to  make  use  of  the  second  property 
namely  the  bending  of  the  current-voltage  characteristic,  a  local 
or ' '  booster  "  battery  is  inserted  in  series  with  the  crystal.  Using  the 
battery  makes  the  crystal  operate  at  a  voltage  which  corresponds 
with  the  sharpest  bend  of  the  curve,  so  that  a  slight  increase  of  volt- 


RADIO   COMMUNICATION.  305 

age  in  one  direction  will  produce  a  fairly  large  increase  of  current, 
while  an  equal  decrease  of  voltage  on  the  crystal  will  produce  a 
relatively  smaller  decrease  of  current. 

The  application  is  made  clear  in  Fig.  239.  Suppose  the  crystal 
used  with  a  booster  battery  adjusted  to  supply  2  volts  to  the  circuit. 
Consider  this  circuit  to  be  subjected  to  incoming  electric  waves 
which  produce  a  small  emf.,  say  0.5  volts,  periodically  added  and 
subtracted.  Curve  a  represents  the  voltage  induced  in  the  cir- 
cuit by  the  incoming  waves.  The  resultant  voltage  wave  acting  on 
the  crystal  is  at  each  instant  two  volts  greater  than  the  value  of 
the  induced  emf.,  and  is  represented  by  curve  6.  Under  the  instan- 
taneous applied  emf.  of  1.5  volts,  shown  at  point  p  in  curve  6,  the 
crystal  will  allow  a  current  of  2  microamp.  to  pass  as  shown  in  Fig. 
239-c;  for  2  volts  in  curve  b  a  current  of  4  microamp.  will  pass 
as  shown  in  Fig.  239-c,  and  for  2.5  volts  a  current  of  8  microamp. 
will  pass.  Curve  c  represents  the  condition  which  would  exist 
in  a  circuit  containing  no  inductance.  The  actual  current  wave 
through  the  telephone,  as  smoothed  out  by  the  inductance  of  the 
telephone  and  the  other  inductance  of  the  circuit,  is  shown  in 
curve  d.  In  this  discussion  the  curves  are  shown  for  the  case  where 
the  incoming  waves  are  undamped.  The  average  value  of  the  cur- 
rent d  is  somewhat  above  4  microamp.  during  the  time  the  incoming 
wave  group  is  acting.  Between  groups  it  drops  to  just  4  microamp. 
(with  2  volts  applied).  Thus  the  current  comes  in  pulses  which  will 
cause  a  sound  to  be  emitted  by  the  telephone.  This  sound  will  be 
determined  by  the  number  of  wave  trains  received  per  second. 
These  may  be  groups  of  damped  waves,  or  continuous  waves  broken 
up  by  a  tikker. 

180.  Telephone  Eeceivers. — The  distinctive  features  of  telephone 
receivers  for  radio  work  are  lightness  of  the  moving  parts  and  the 
employment  of  a  great  many  turns  of  wire  around  the  magnet  poles. 
The  lightness  of  the  moving  parts  enables  them  to  follow  and  respond 
to  rapid  pulsations  of  current.  The  large  number  of  turns  of  wire 
causes  a  relatively  large  magnetic  field  to  be  produced  by  a  feeble 
current.  The  combined  effect  is  to  give  a  very  sensitive  receiving 
device.  Inasmuch  as  the  size  of  wire  used  is  always  about  the  same 
(around  A.W.G.  No.  40  copper),  the  amount  of  wire  and  therefore 
the  number  of  turns  is  usually  specified  indirectly  by  stating  the 
number  of  ohms  of  resistance  in  the  coils.  Telephone  receivers  of 
fair  sensitiveness  for  radio  work  have  1000  ohms  in  each  receiver 
97340  °— 19 20 


306  RADIO   COMMUNICATION. 

(measured  on  direct  current),  while  the  better  ones  usually  have  1500 
to  2000  ohms  per  receiver. 

The  most  common  type,  called  the  magnetic  diaphragm  type,  has 
a  U-shaped  permanent  magnet  with  soft  iron  poles,  and  a  thin  soft 
iron  diaphragm  very  close  to  the  poles  so  that  it  vibrates  when  the 
attraction  is  rapidly  varied,  producing  sounds  to  correspond  with  the 
frequency  of  the  pulsations  of  current.  See  Section  60. 

The  only  other  important  type  is  called  a  mica  diaphragm  receiver. 
The  regular  diaphragm  is  of  mica,  and  is  put  in  the  usual  place  in 
the  receiver,  but  of  course  is  not  acted  upon  directly  by  the  magnets. 
Between  the  magnet  poles  a  soft  iron  armature  is  pivoted,  inside  of 
a  solenoidal  telephone  winding.  It  is  arranged  so  that  as  it  moves 
in  response  to  changes  of  magnetism  a  small  stiff  wire  attachment 
transmits  the  motion  to  the  mica  diaphragm.  The  armature  is  so 
arranged  that  there  is  no  pull  upon  it  at  all  except  when  pulsations 
of  current  are  passing  through  the  coil.  This  is  contrary  to  the  ordi- 
nary magnetic  telephone  receiver  where  the  magnet  poles  are 
always  exerting  a  pull  on  the  diaphragm.  If  there  is  no  strain  in 
the  diaphragm  between  pulsations  the  vibratory  movements  due  to 
incoming  signals  are  much  greater  than  if  a  strain  were  already 
existing  in  the  diaphragm  or  armature.  In  the  mica  telephone  this 
unrestrained  vibration  is  communicated  to  the  mica  diaphragm  near 
the  ear.1 

Impedance. — The  impedance  of  a  telephone  receiver  to  alternating 
current  increases  rapidly  with  frequency,  and  at  radio  frequency  is 
so  great  as  to  permit  practically  no  current  to  pass.  By  the  use  of 
detectors,  however,  the  current  that  passes  in  the  telephone  consists 
of  a  series  of  pulses  of  audio  frequency,  usually  from  500  to  1200 
pulses  or  vibrations  per  second.  A  typical  telephone  receiver 
having  a  direct  current  impedance  (resistance)  of  2000  ohms  was 
found  at  400  cycles  per  second  to  have  an  impedance  of  2900  ohms, 
and  at  800  cycles  an  impedance  of  3900  ohms,  rising  to  4400  ohms 
at  1000  cycles  per  second. 

181.  Beceiving  Coils  and  Condensers. — The  coils  used  in  receiv- 
ing apparatus  are  very  simple  in  construction,  being  usually  wound 
in  a  single  layer  of  wire  on  a  bakelite,  pasteboard,  or  other  insulating 
tube.  The  wire  is  usually  stranded  and  covered  with  an  insulation 
of  silk  or  cotton.  In  some  types  one  or  two  sliders  make  contact 
with  any  desired  turn  of  wire,  the  insulation  being  scraped  off  on 

1  For  a  detailed  account  and  tracing  out  of  the  magnetic  circuits  see  Bucher's  Prac- 
tical Wireless  Telegraphy,  page  168. 


RADIO   COMMUNICATION. 


307 


top  of  the  wires  along  a  narrow  path  lengthwise  of  the  coil.  The 
more  common  field  sets  use  no  slider  but  have  switches  whose  points 
are  connected  by  tap  wires  to  the  turns  of  wire  in  the  coil.  One 
switch  takes  care  of  single  turns,  and  the  other  switch  makes  contact 
to  groups  of,  say,  ten  turns  each.  To  cover  100  turns,  for  instance, 
one  switch  should  have  9  points  of  ten  turns  each,  and  a  zero  point, 
making  10  points  in  all,  and  the  units  switch  would  also  have  9  points, 


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and  a  zero  point.  Then  any  number  from  0  to  100  turns  could  be 
used.  If  a  coil  had  400  turns  the  first  switch  in  groups  of  20  turns 
could  have  20  points  including  zero,  and  the  unit  switch  could  also 
have  20  points  for  nineteen  unit  turns  and  zero. 

Fig.  240  shows  two  receiving  transformers,  in  one  of  which  the 
primary  adjustment  is  made  by  a  slider  touching  each  turn  of  wire, 
and  the  secondary  adjustment  is  made  by  a  switch  in  groups  of  30 


308  RADIO    COMMUNICATION. 

to  40  turns.  The  finer  secondary  tuning  is  done  by  a  variable  con- 
denser. The  coupling  between  the  coils  is  loosened  by  pulling  the 
secondary  out  of  the  primary.  The  other  receiving  transformer  has 
control  of  both  coils  by  switches. 

Loading  coils  are  merely  large  coils  used  to  increase  the  induc- 
tance of  the  circuit  when  the  inductance  of  the  receiving  transformer 
is  not  great  enough  to  be  tuned  to  the  wave  length  received.  Ordi- 
nary tuning  coils  and  the  coils  of  receiving  transformers  of  the 
inductively  coupled  type  are  usually  12  to  20  cm.  long  and  8  to  12 
cm.  in  diameter,  with  single  layer  windings,  while  some  of  the  com- 


FIG.  241.— Rotary  variable  air  condenser. 

mon  loading  coils  for  long  waves  are  50  cm.  or  more  in  length.  The 
inductance  of  the  12  cm.  coils  runs  from  1000  to  5000  microhenries, 
while  the  large  loading  coils  have  in  the  neighborhood  of  50  milli- 
henries. The  inductance  of  any  particular  coil  can  be  calculated 
by  reference  to  Section  170. 

Fig.  241  shows  a  type  of  variable  condenser  with  air  dielectric, 
which  is  generally  used.  The  maximum  capacitance  is  usually 
0.0005  mfd.,  adjustable  to  a  minimum  of  nearly  zero.  A  set  of  semi- 
circular metal  plates  is  rotated  between  a  corresponding  set  of  fixed 


RADIO    COMMUNICATION. 


309 


plates,  forming  alternate  layers  of  air  dielectric  with  adjacent  con- 
ductors of  opposite  polarity.  In  working  with  vacuum  tubes  most 
of  the  tuning  is  done  with  variable  condensers.  In  the  primary 
it  sometimes  happens  that,  with  continuous  waves,  the  tuning  must 


FIG.  242.— Simple  receiving  set  (type  SCR-54-A)  of  the  portable,  cabinet  type. 

be  closer  than  that  afforded  by  single  turns  of  the  primary  coil,  so  a 
variable  condenser  is  placed  in  parallel  with  the  coil  and  used  for 
fine  tuning. 

Fig.  242  shows  a  typical  simple  receiving  set  in  cabinet  form, 
with  the  tap  switches  and  variable  condensers,  and  a  handle  for 
changing  the  coupling  between  primary  and  secondary  coils. 


310  RADIO    COMMUNICATION. 

182.  Measurement  of  Received  Current. — It  is  possible  to  measure 
current  received  in  a  radio  receiving  set  by  the  use  of  a  crystal 
detector  and  a  galvanometer.  This  is  a  rather  delicate  experiment, 
and  information  regarding  it  is  given  in  C.  74,  pages  167  to  170.  The 
method  ordinarily  used  is  the  shunted  telephone  method.  A  resis- 
tance is  placed  in  parallel  with  the  telephone  and  reduced  until  the 
limit  of  audibility  in  the  telephone  is  reached,  that  is,  until  the 
sound  in  the  telephone  becomes  so  weak  that  the  operator  can  just 
barely  distinguish  dots  and  dashes.  If  t  is  the  impedance  of  the 
telephone  for  the  frequency  of  the  current  impulses  through  it,  s  the 
impedance  of  the  shunt,  It  the  least  current  in  the  telephone  which 
gives  an  audible  sound ,  and  /  the  total  current  flowing  in  the  com- 
bination of  the  telephone  and  shunt, 

/     s+t 

4=~r 

This  ratio,  s+t  to  s,  is  called  the  "audibility."  It  can  be  expressed 
in  units  of  current  if  properly  calibrated.  It  is  ordinarily  used  in 
making  rough  comparative  measurements.  It  is,  of  course,  affected 
by  the  sensitiveness  of  the  operator's  ear. 

For  detecting  currents  of  the  order  of  0.0001  amp.,  the  crystal 
detector  and  telephone  are  used;  for  0.000001  amp.,  the  ordinary 
vacuum  tube  and  telephone  are  used;  for  0.00000001  amp.,  the 
vacuum  tube  connected  for  regenerative  amplification  and  telephone 
are  used. 


CHAPTER  6. 

VACUUM  TUBES  IN  RADIO  COMMUNICATION.1 

183.  Introduction. — The  advent  of  vacuum  tubes,  sometimes  called 
electron  tubes,  has  resulted  in  great  advances  in  radio  communica- 
tion.    As  such  tubes  may  be  used  for  a  variety  of  purposes,  to  gener- 
ate, to  amplify,  and  to  modulate  radio  oscillations,  as  well  as  to 
detect  them,  they  are  now  used  in  most  types  of  radio  apparatus. 
New  applications  have  come  rapidly,  and  possibilities  of  further 
developments  are  most  promising.     One  fact  of  importance  is  that 
such  tubes  make  possible  the  use  of  apparatus  that  is  easily  porta- 
ble— a   primary   consideration    in   military   communication.    The 
principles  underlying  the  uses  of  vacuum  tubes,  and  their  operation 
under  the  widely  different  conditions  met  in  actual  practice,  there- 
fore deserve  careful  study. 

A.  Electron  Flow  in  Vacuum  Tubes. 

184.  Current  in  a  Two-Electrode  Tube. — If  two  wires  are  con- 
nected to  a  battery,  one  to  each  terminal,  the  other  ends  may  be 
brought  very  close  together,  in  air,  yet  so  long  as  they  do  not  touch, 
no  current  flows  between  them.    The  two  ends  may  be  enclosed  in  a 
bulb  like  that  of  an  incandescent  lamp,  and  the  air  pumped  out, 
leaving  a  vacuum,  and  still  so  long  as  the  ends  are  separated,  no  cur- 
rent flows.     A  common  experience  illustrates  this.     When  the  fila- 
ment in  an  electric  lamp  breaks,  the  current  stops  and  the  light  goes 
out.     But  if  one  of  the  two  wire  ends  mentioned  above  is  heated  to  a 
bright  red,  or  hotter,  it  is  an  interesting  fact  that  a  current  can  be 
made  to  flow  across  the  apparently  empty  space  between  them. 

Call  the  two  ends  of  wire  the  "electrodes."  The  current  between 
the  hot  and  the  cold  electrode  is  made  possible  by  the  electrons  given 
off  by  the  hot  electrode  (explained  further  in  the  next  paragraph), 
and  is  a  large  enough  current  to  be  measured  by  sensitive  instru- 
ments and  to  have  highly  important  uses  in  radio  communication. 

i  See  also  S.  C.  Radio  Pamphlet  No.  1,  Part  2. 

311 


312  RADIO    COMMUNICATION. 

The  question  will  perhaps  arise  as  to  how  a  single  electrode  can  be 
heated  when  it  is  inside  of  a  glass  bulb.  That  is  readily  done  by 
shaping  it  into  a  loop,  of  which  both  ends  are  brought  through  the 
base  of  the  bulb.  These  ends  are  connected  to  a  battery  of  a  few  cells, 
the  current  from  which  heats  the  loop  like  an  ordinary  incandescent 
lamp  filament.  Thus  one  of  the  electrodes  becomes  a  hot  filament. 
For  the  other  electrode  a  little  plate  of  metal  is  used.  A  bulb  con- 
taining a  hot  and  a  cold  electrode  as  described  forms  a  ''two-elec- 
trode vacuum  tube." 

The  action  of  these  vacuum  tubes  depends  upon  the  fact  that 
when  a  metal  is  heated  in  a  vacuum  it  gives  off  electrons  into  the 
surrounding  space.  (See  Section  6.)  As  the  electrons  have  a  nega- 
tive charge,  the  charge  remaining  on  the  metal  is  positive,  therefore 
few  of  the  electrons  go  very  far,  but  are  attracted  back  to  the  metal 
so  that  there  is  a  kind  of  balance  established  between  the  outgoing 
and  the  returning  electrons.  Now  suppose  a  battery  is  connected 
between  the  two  electrodes,  filament  and  plate.  This  battery  is  B 
in  Fig.  243,  and  is  so  connected  as  to  make  the  plate  potential  posi- 
tive with  respect  to  the  filament.  The  electrons,  consisting  of 
negative  electricity,  are  attracted  by  the  plate  P,  are  captured  by 
by  it,  and  return  no  more  to  the  filament  F.  Thus  the  battery 
causes  a  continuous  flow  of  electrons  (negative  electricity)  from  the 
filament  to  the  plate;  that  is,  an  electric  current  is  flowing  in  the 
space  between  them. 

The  current  ceases  when  the  filament  is  cold,  because  no  electrons 
are  then  escaping  from  the  metal.  No  current  will  flow  if  the  battery 
is  wrongly  connected,  since,  when  the  plate  is  negative  with  respect 
to  the  filament,  the  negative  charge  of  the  plate  will  repel  the 
electrons  back  into  the  filament. 

The  distinction  between  direction  of  current  and  direction  of 
electron  flow  must  be  carefully  noted.  It  happens  that  for  a  great 
many  years  the  direction  from  the  positive  toward  the  negative 
terminal  has  been  arbitrarily  called  the  direction  of  the  current. 
Now  it  is  found  that  these  little  electrons  travel  from  the  negative 
toward  the  positive  electrode.  The  direction  of  current  and  the 
direction  of  motion  of  the  electrons  are  therefore  opposite. 

lonization. — The  above  explanation  of  the  mechanism  of  the 
flow  of  current  between  the  filament  and  plate  (commonly  called 
the  "plate  current")  in  a  vacuum  tube  applies  to  the  case  where 


RADIO   COMMUNICATION. 


313 


the  vacuum  is  very  complete.  If  there  is  more  than  the  merest 
trace  of  gas  remaining  in  the  tube,  the  operation  is  more  complicated, 
and  a  larger  current  will  usually  flow  with  the  same  applied  voltage. 
This  happens  in  the  following  manner. 

In  a  rarefied  gas,  some  of  the  electrons  present  are  constituent 
parts  of  atoms  and  some  are  free.    These  free  electrons  move  about 


Plate    Volt»k« 


stic.  curves  of  A  two - 
eUetrode.  tuba  for  two  different 
T«*m|3«  nature* 


vacuum 
F  -  FiUment 
P  -  Plate 
A-  Battery  for 

•filament 
£>-  &*Ttery  (or  sending 
current  -thro  aj>ace  befw«.n 
f^ate  *nd  f  lament 


Fi  IA  ma.rvf    T«m  fr«.ratore> 


Characteristic   curve*   of<itwo- 
e|eetro<J«  tube   -for  two  different 


with  great  velocity,  and  if  one  of  them  strikes  an  atom,  it  may  dis- 
lodge another  electron  from  the  atom.  Under  the  action  of  the  emf. 
between  plate  and  filament,  the  newly  freed  electron  will  acquire 
velocity  in  one  direction  (that  of  the  colliding  electron)  and  the 


314  RADIO   COMMUNICATION. 

positively  charged  remainder  of  the  atom  will  move  in  the  opposite 
direction.  Thus  both  of  the  parts  of  the  disrupted  atom  become 
carriers  of  electricity  and  contribute  to  the  flow  of  current  through 
the  gas.  This  action  of  a  colliding  electron  upon  an  atom  is  called 
"ionization  by  collision",  and  on  account  of  it  relatively  large  plate 
currents  are  obtained  in  vacuum  tubes  having  a  poor  vacuum. 
The  earlier  "audion"  tubes  were  of  this  sort,  but  tubes  are  now,  as 
a  rule,  made  with  better  vacua  than  formerly,  so  that  ionization 
by  collision  is  responsible  for  but  a  small  part  of  the  current  flow. 

At  first  it  would  seem  to  be  an  advantage  to  have  ionization  by 
collision,  because  a  larger  plate  current  can  be  obtained,  but  there 
are  two  difficulties  which  have  proved  so  great  that  tubes  are  now 
usually  made  to  have  only  the  pure  electron  flow.  The  first  of 
these  difficulties  is  a  rapid  deterioration  of  the  filament  when  a 
large  plate  current  flows.  The  positively  charged  parts  of  the 
atoms  are  driven  violently  against  the  negatively  charged  filament, 
and  since  they  are  much  more  massive  than  electrons  (an  oxygen 
or  nitrogen  ion  has  about  25,000  times  the  mass  of  an  electron)  this 
bombardment  actually  seems  to  tear  away  the  surface  of  the  fila- 
ment. The  second  disadvantage  of  tubes  with  poor  vacuum  is 
that  too  large  a  battery  voltage  may  cause  a  "blue  glow"  discharge; 
the  difficulties  connected  with  the  presence  of  this  visible  kind  of 
current  flow  are  mentioned  in  Section  191. 

185.  Actual  Forms  of  Two-Electrode  Tubes. — A  tube  similar  to 
that  described  above  was  the  earliest  used  in  radio  practice.  It 
was  called  the  "Fleming  valve."  It  rectifies  a  high-frequency 
current  somewhat  as  a  crystal  detector  (Section  179)  does.  This 
rectifying  action  takes  place  because  a  current  flows  when  the 
negative  terminal  of  a  battery  is  applied  to  the  heated  filament 
and  the  positive  one  to  the  plate,  whereas  the  current  becomes 
practically  zero  if  the  battery  connection  is  reversed.  The  latter 
happens  because  the  negatively  charged  plate  repels  the  negative 
electrons  and  stops  the  current  flow.  The  Fleming  valve  was  used 
as  a  detector,  but  has  been  replaced  by  the  three-electrode  tube 
discussed  below  because  the  latter  has  proved  to  be  much  more 
sensitive. 

Another  type  of  two-electrode  tube  is  the  "kenotron,"  developed 
by  the  General  Electric  Co.  It  has  a  much  better  vacuum  than 
the  Fleming  valve,  and  is  made  in  larger  dimensions.  It  is  used  as 
a  rectifier  of  currents  of  high  voltage  and  low  frequency.  It  changes 


RADIO   COMMUNICATION.  315 

alternating  current  into  a  pulsating  current  all  in  one  direction. 
Small  currents  (well  below  1  amp.)  are  rectified  by  these  tubes,  and 
power  up  to  several  kilowatts  can  be  handled  even  if  the  applied 
voltage  exceeds  25,000. 

A  third  form  of  two-electrode  tube,  which  promises  to  be  useful 
for  military  purposes,  is  the  "tungar  rectifier."  1  These  tubes  con- 
tain rarefied  argon  gas  and  their  relatively  large  currents  are  pro- 
duced mainly  through  ionization  by  collision.  These  are  useful  for 
charging  storage  batteries  from  a  110- volt  a.c.  line.  One  size  charges 
a  battery  of  from  6  to  12  volts  at  from  1  to  2  amp. ;  a  larger  size  charges 
a  6  or  12  volt  battery  at  6  amp. 

186.  The  Three-Electrode  Vacuum  Tube. — A  great  improvement 
upon  the  two-electrode  tube  for  radio  purposes,  consists  in  the  addi- 
tion of  a  third  electrode,  inside  the  tube,  in  the  form  of  a  metallic 
gauze  or  "grid"  of  fine  wires  between  the  filament  and  the  plate. 
This  makes  it  possible  to  increase  or  decrease  the  current  between 
plate  and  filament  through  wide  limits.  It  is  important  to  under- 
stand how  this  result  is  obtained. 

It  is  necessary  first  to  consider  what  happens  in  a  two-electrode 
tube  having  a  good  vacuum,  when  either  the  voltage  of  the  battery 
B  or  the  temperature  of  the  filament  is  varied. 

Effect  of  Plate  Voltage. — Suppose  first  that  the  filament  tempera- 
ture is  kept  constant.  Then  a  definite  number  of  electrons  will  be 
sent  out  per  second.2  The  number  of  electrons  that  travel  across 
the  tube  and  reach  the  plate  per  second  determines  the  magnitude 
of  the  current  through  the  plate  circuit.  The  number  of  electrons 
that  reach  the  plate  increases  as  the  voltage  of  the  battery  B  in- 
creases. If  this  voltage  is  continuously  increased,  a  value  will  be 
reached  at  which  all  the  electrons  sent  out  from  the  filament  arrive 
at  the  plate.  No  further  increase  of  current  is  possible  by  increasing 
the  voltage  and  this  current  is  called  the  saturation  current.  This 
is  illustrated  in  Fig.  244,  (full  line  curve)  which  shows  that  when 
the  voltage  applied  to  the  plate  is  small,  (horizontal  distance)  the 
current  flowing  between  filament  and  plate,  called  the  "plate  cur- 
rent" (vertical  distance)  is  also  small,  but  if  the  voltage  is  made 

1  R.  E.  Russell— General  Electric  Review,  20,  p.  209;  1917. 

2  The  law  giving  the  number  of  electrons  emitted  per  second,  as  it  depends  upon 
the  temperature  of  the  filament,  was  first  given  by  O.  W.  Richardson,  whose  book, 
"The  Emission  of  Electricity  from  Hot  Bodies"  (1916)  describes  his  experiments  in 
great  detail.    See  also  J.  J.  Thomson,  "Conduction  of  Electricity  through  Gases," 
p.  161,  and  I.  Langmvir,  Physical  Review,  2,  p.  450;  1913. 


316  RADIO    COMMUNICATION. 

larger,  the  plate  current  increases  more  rapidly  than  the  voltage, 
up  to  a  certain  value.  The  bend  in  the  curve  shows  that  when  the 
voltage  has  been  made  large  enough,  there  is  little  further  gain  in 
current. 

If  now  the  temperature  of  the  filament  is  raised  by  means  of  the 
heating  battery  to  a  higher  constant  value  and  the  same  voltage 
steps  again  applied,  the  plate  current  curve  will  coincide  with  that 
obtained  before,  until  the  bend  is  reached,  then  it  will  rise  higher, 
as  shown  by  the  dotted  portion  of  the  curve  in  the  Fig.  244.  The 
explanation  of  this  is  that  the  number  of  electrons  sent  out  by  the 
filament  increases  with  the  temperature,  approximately  as  the 
square  of  the  excess  of  filament  temperature  above  red  heat,  and 
thus  more  are  available  to  be  drawn  over  to  the  plate.  Thus  a 
higher  value  of  plate  current  will  be  obtained  before  reaching  the 
limiting  condition  when  all  the  electrons  emitted  arrive  at  the 
plate.  When  this  finally  happens  the  curve,  as  before,  bends  over 
until  nearly  horizontal. 

Effect  of  Filament  Temperature. — Suppose  now  that  the  voltage 
of  battery  B  is  kept  at  a  constant  value  Vl ,  and  the  filament  tempera- 
ture gradually  raised  by  increasing  the  current  from  the  heating 
battery.  The  number  of  electrons  sent  out  will  continue  to  increase 
as  the  temperature  rises.  The  electric  field  intensity  (Section  33) 
due  to  the  presence  of  the  negative  electrons  in  the  space  between 
filament  and  plate  may  at  last  equal  and  neutralize  that  due  to  the 
positive  potential  of  the  plate  so  that  there  is  no  force  acting  on  the 
electrons  near  the  filament.  This  effect  of  the  electrons  in  the 
space  is  called  the  "space  charge  effect."  It  must  not  be  sup- 
posed that  the  space  charge  effect  is  caused  by  the  same  electrons  all 
the  time.  Electrons  near  the  plate  are  constantly  entering  it,  but 
new  electrons  emitted  by  the  filament  are  entering  the  space,  so 
that  the  total  number  between  filament  and  plate  remains  constant 
at  a  given  temperature.  After  the  temperature  of  the  filament  has 
reached  the  point  where  the  effect  of  the  electrons  present  in  the 
space  between  filament  and  plate  neutralizes  the  effect  of  the  plate 
voltage,  any  further  increase  of  the  filament  temperature  is  unable 
to  cause  an  increase  of  the  current.  The  tendency  of  the  filament  to 
emit  more  electrons  per  second,  because  of  the  increased  tempera- 
ture, is  offset  by  the  increase  in  space  charge  effect,  which  would 
result  if  electrons  were  emitted  more  rapidly;  or,  more  exactly,  for 
any  extra  electrons  emitted,  an  equal  number  of  those  in  the  space 
are  repelled  back  into  the  filament.  If  now  the  plate  voltage  is  in- 


RADIO   COMMUNICATION.  317 

creased  to  a  new  value  F2,  the  plate  current  curve  will  rise  higher 
before  bending  over  as  shown  by  the  dotted  portion  of  the  curve  in 
Fig.  245,  because  it  takes  a  larger  space  charge  to  offset  the  effect 
of  the  plate  at  the  higher  voltage. 

187.  Effect  of  Grid. — In  the  three-electrode  tube,  the  additional 
electrode,  or  grid,  is  interposed  between  filament  and  plate,  in  the 
stream  of  electrons  which  constitute  the  plate  current.     If  a  voltage 
is  impressed  upon  it  by  means  of  a  third  battery,  shown  at  C  in  Fig. 
246,  this  modifies  the  space  charge  effect.    The  electrons  traveling 
from  filament  to  plate  pass  between  the  grid  wires.     If  the  grid 
is  given  a  potential  more  negative  than  the  filament,  it  will  repel 
the  electrons,  but  many  of  them  will  still  pass  through,  owing  to  their 
high  velocity,  and  reach  the  plate.     If  the  grid  potential  is  made 
still  more  negative,  the  plate  current  will  diminish  until  finally  it 
may  be  stopped  completely. 

Suppose,  however,  the  grid  is  given  a  positive  potential  instead 
of  negative.  More  electrons  are  now  drawn  toward  the  plate  than 
would  otherwise  pass,  and  the  plate  current  increases.  The  grid 
charge  partially  neutralizes  the  effect  of  the  space  charge.  As  in 
the  two-electrode  tube,  a  limit  to  the  magnitude  of  the  plate 
current  will  finally  be  reached,  when  the  space  charge  due 
to  the  large  number  of  negative  electrons  in  the  tube,  fully  coun- 
teracts the  influence  of  the  positive  charges  on  grid  and  plate. 
The  attainment  of  the  limiting  or  saturation  value  of  the  plate  current 
is  assisted  by  the  absorption  of  more  electrons  into  the  grid  if  its 
positive  potential  is  increased.  This  absorption  gives  rise  to  a 
very  small  current  in  the  circuit  FGCF  (Fig.  246)  which  is  called 
the  grid  current.  The  total  electron  flow  is  the  sum  of  the  plate 
current  and  the  grid  current.  As  the  potential  of  the  grid  is  made 
more  and  more  positive,  more  and  more  electrons  will  be  absorbed. 

188.  Characteristic  Curves. — The  above  principles  may  be  illus- 
trated by  curves  obtained  by  experiment,  known  as  the  character- 
istic curves  of  a  vacuum  tube. 

One  form  of  these  curves  shows  the  relation  between  plate  current 
and  grid  voltage.  For  example,  a  certain  tube  was  tested  by  keep- 
ing the  filament  at  a  constant  temperature  by  a  steady  current 
through  it  from  battery  A  (Fig.  246).  A  constant  voltage  of  35  volts 
between  plate  and  filament  was  maintained  by  the  battery  B,  and 
varying  voltages  from  0  to  7  volts  were  applied  to  the  grid  G  by  the 
battery  C.  For  each  value  of  grid  voltage  the  current  flowing 


318 


RADIO    COMMUNICATION. 


between  filament  and  plate  was  noted  in  the  microammeter  M. 
The  result  is  plotted  in  Fig.  247  and  in  the  upper  curve  of  Fig.  248. 
It  shows  that  as  the  grid  voltage  increases  from  —3  to  +7  volts, 


PWe 


FIQ.  Z47 

stlc  curves  of  PUta 
id  Currants  at  A  -singla 
Volt*i« 


FIG.  244 


yVTTA'TV 


1/..U.V. 


the  (state  current  for  three  different   {joints 
of  the  |slat«  current  ckinaoteriaric.. 


the  plate  current  increases  from  zero,  slowly  at  first,  then  more 
rapidly,  but  above  2  volts  more  slowly  again.  Similar  tests  with 
lower  plate  voltages,  30  volts  and  25  volts  respectively,  gave  similar 


RADIO   COMMUNICATION.  319 

results  except  that  the  plate  currents  were  smaller,  as  shown  in  the 
two  other  full  line  curves  of  Fig.  248. 

Another  important  characteristic  curve  shows  the  relation  between 
grid  current  and  grid  voltage.  This  curve  is  also  shown  in  Figs. 
247  and  248.  It  is  at  once  evident  that  the  grid  current  is  very  small 
in  comparison  with  the  plate  current.  In  order  to  get  a  clearer 
idea  of  the  dependence  of  the  grid  current  on  the  grid  voltage,  it 
is  customary  to  draw  the  grid  current  to  a  magnified  scale.  For 
example,  the  grid  current  measurements  made  in  the  above  men- 
tioned case  when  the  plate  voltage  was  held  at  30  volts,  are  shown 
in  Fig.  248  to  such  a  scale  that  the  same  vertical  distance  which 
represents  200  microamp.  of  plate  current  indicates  only  5  microamp. 
of  grid  current.  Note  that  the  grid  current  is  zero  for  a  very  small 
negative  grid  voltage,  but  rapidly  increases  with  increasing  posi- 
tive grid  voltage. 

189.  Effect  of  an  Alternating  Emf.  Applied  to  Grid. — It  is  evident 
from  these  curves  that  if  an  alternating  emf .  is  applied  to  the  grid 
(that  is,  if  it  is  made  alternately  +  and  — ),  the  plate  current  will 
periodically  increase  and  decrease,  keeping  step  with  the  variations 
in  grid  emf.  Suppose  the  grid  potential  to  be  the  same  as  that  of 
the  filament  (grid  voltage  zero  in  Fig.  246)  the  upper  curve  of  the 
figure  shows  that  the  value  of  the  plate  current  will  be  100  microamp. 
when  there  are  35  volts  on  the  plate.  Then  if  an  alternating  emf. 
of  1  volt  (maximum  value)  is  impressed  between  grid  and  filament, 
the  plate  current  will  keep  changing  from  the  value  of  the  ordi- 
nate  of  point  b  (Fig.  248)  to  that  of  point  c,  that  is,  from  about  250 
to  about  50  microamp. 

Thus  an  increase  of  one  volt  in  the  emf.  applied  to  the  grid 
produces  an  increase  in  the  plate  current  of  150  milliamp.  (from 
100  to  250),  while  a  decrease  of  the  same  amount  in  grid  voltage 
causes  a  reduction  of  only  50  milliamp.  The  effect  then  of  applying 
a  high  frequency  oscillating  voltage  to  the  grid  will  be  to  cause  a 
higher  "average"  value  of  plate  current  during  the  time  of  such 
voltage  application.  The  preceding  discussion  relates  to  what 
happens  when  the  points  a,  6,  and  c  are  on  the  lower  bend  of  the 
characteristic  curve.  When  the  grid  voltage  is  so  adjusted  that 
the  plate  current  has  a  value  somewhere  on  the  upper  bend  of  the 
characteristic  curve,  the  effect  of  applying  an  oscillating  voltage 
to  the  grid  will  again  be  to  cause  oscillations  of  the  plate  current. 
Here,  however,  the  effect  of  the  alternating  grid  voltage  is  to  cause 


320  RADIO   COMMUNICATION. 

a  "lower"  average  value  of  the  plate  current.  If  the  grid  voltage 
is  adjusted  to  such  a  value  that  the  plate  current  assumes  a  value 
on  the  straight  portion  of  the  characteristic  (say  point  P,  Fig.  247), 
oscillations  of  the  grid  voltage  cause  oscillations  of  the  plate  current, 
but  the  average  value  of  the  plate  current  is,  in  this  case,  unchanged. 

These  facts  are  shown  in  Fig.  249.  At  the  left  is  represented  the 
plate  characteristic,  and  three  points  A,  B,  and  C  are  designated, 
on  the  lower  bend,  straight  portion  and  upper  bend,  respectively. 
To  the  right  is  shown  the  effect  of  an  alternating  grid  voltage  in 
each  case.  The  dotted  lines  represent  the  original  values  of  the  plate 
current.  The  full  curves  show  the  oscillations  of  plate  current,  caused 
by  the  oscillations  of  the  grid  voltage,  and  the  full  straight  lines 
the  average  plate  current  during  these  oscillations.  As  will  be  shown 
later,  cases  A  and  C  represent  conditions  suitable  for  use  of  the  tube 
as  a  detector,  and  B  the  condition  for  use  as  an  amplifier.  There 
is  no  appreciable  time  lag  between  grid  voltage  and  plate  current 
and  thus  no  phase  difference,  even  when  the  frequency  of  alter- 
nation is  several  million  per  second. 

With  different  kinds  of  tubes  different  values  of  the  grid  voltage 
are  necessary,  in  order  to  obtain  a  value  of  plate  current  at  the 
desired  part  of  the  characteristic.  This  adjustment  is  accom- 
plished by  the  C  battery  in  the  grid  circuit  (Fig.  246).  Since  the 
plate  current  is  so  sensitive  to  small  changes  of  grid  voltage,  it  is 
often  desirable  to  provide  a  voltage  divider  on  the  C  battery  to 
facilitate  the  close  adjustment  of  the  grid  voltage.  In  C.  74, 
p.  203,  is  illustrated  such  an  arrangement  which  is  useful  in 
experimental  determinations  of  the  characteristic  curves. 

190.  Practical  Forms  of  Three-Electrode  Tubes.1 — In  Fig.  250  are 
shown  a  number  of  French  and  American  tubes.  Those  in  (A)  are 
French.  The  two  smallest  tubes  are  the  ones  most  commonly  used; 
they  serve  for  detectors,  amplifiers,  and  generators.  The  one  with 
two  projections  is  used  for  short  wave  length  apparatus,  the  idea 
of  the  construction  being  to  keep  the  connections  to  grid  and  plate 
as  widely  separated  as  possible,  to  minimize  capacitance  between 
them.  Both  types  have  a  straight  filament,  the  grid  is  a  spiral  wire 
surrounding  the  filament,  and  the  plate  is  a  cylinder  surrounding 
both.  A  number  of  Western  Electric  Co.  tubes  are  shown  in  (B) 
General  Electric  Co.  tubes  (called  by  that  company  "pliotrons") 
in  (C),  and  DeForest  Radio  Telephone  and  Telegraph  Co.  tubes 
(called  by  that  company  "audions")  in  (D).  The  DeForest  Co. 

i  See  also  Electrical  World  for  Feb.  22, 1919,  Vol.  73,  No.  8;  article  by  Capt.  Ralph 
Bown. 


fit 


1 1 1 

^P  B   Bp      ^IP 


FIG.  250.— French  and  American  vacuum  tubes. 
97340° — 19 21  321 


322 


RADIO    COMMUNICATION. 


makes  larger  tubes,  called  "oscillions."  In  all  modern  American 
tubes  the  filament  is  a  wire  doubled  back  one  or  more  times;  the 
grid  is  a  pair  of  metal  lattices,  one  on  each  side  of  the  filament; 
and  the  plate  is  a  pair  of  metal  planes  parallel  to  the  two  parts  of 
the  grid.  The  larger  tubes  are  used  as  generators  of  radio  current 

B.  The  Vacuum  Tube  as  a  Detector. 

191.  Simple  Detector  Circuit  and  Explanation  of  its  Action. — In 
order  to  understand  how  a  vacuum  tube  acts  when  used  as  a  detector, 
consider  the  circuit  shown  in  Fig.  251.  Suppose  the  receiving 
antenna  picks  up  a  signal.  Oscillations  in  the  tuned  circuit  L  C1  are 
set  up,  because  L  is  inductively  coupled  to  the  antenna  circuit.  The 


Fl<3  Z5Z|  M^Afe8  oscillations   impressed  on  the  jrid 
I  (£)  Resulting  variations  in  t>l«te  oorr.nt 

•uat,ons  <f  fele^Ue 

currents 


Connections  for  ufir^ 
VACDom  tube    A-,  &  ->i'm|al« 
cUt«etor 

'         Qround 


Action  of  Vacuum  tuba  &6  deteofor 


radio  frequency  alternating  voltage  between  the  terminals  of  L  is 
impressed  between  the  filament  and  the  grid,  and  (as  was  explained 
in  Section  189)  brings  about  changes  in  the  plate  current.  If  the 
plate  current  is  normally  at  a  point  on  the  bend  of  the  characteristic 
curve,  say  in  the  region  a  to  c,  Fig.  248,  the  increase  of  plate  current 
when  the  grid  voltage  is  positive  is  greater  than  the  decrease  of  plate 
current  when  the  grid  voltage  is  negative.  On  the  average  the  plate 
current  is  increased  while  the  signal  is  passing.  Fig.  252  shows 
graphically  the  simultaneous  values  of  (1)  high  frequency  oscilla- 
tions of  the  grid  current,  (2)  high  frequency  variations  of  plate  cur- 
rent, and  (3)  audio  frequency  fluctuations  of  telephone  current. 
The  frequency  of  the  wave  trains  should  be  within  the  range  of 


RADIO   COMMUNICATION.  323 

audible  sound,  preferably  between  300  and  2000,  because  the  tele- 
phone inductance  smooths  out  each  train  of  high  frequency  oscil- 
lations into  a  single  pulse  and  the  pulse  frequency  must,  therefore, 
be  within  the  audible  range  in  order  that  the  signals  may  be  heard. 

In  some  cases  it  is  necessary  to  use  a  C  battery  between  points/ 
and  g  (Fig.  251),  in  order  to  bring  the  plate  current  to  the  bend  of 
the  characteristic  curve  (Fig.  248).  This,  however,  does  not  change 
the  action;  the  variations  of  the  plate  current  are  brought  about  by 
the  alternating  emf.  between  the  terminals  of  the  coil  L  just  the  same 
as  when  the  C  battery  is  absent.  It  is  interesting  to  note  here  that 
we  are  employing  resonance  in  the  circuit  LQ  to  obtain  as  large 
an  emf.  as  possible  between  the  terminals  of  the  coil  and  condenser 
with  a  given  signal  (see  Section  109). 

If  the  grid  battery  voltage  is  adjusted  so  that  the  plate  current  has 
a  value  near  the  upper  bend  of  the  plate  current-grid  voltage  curve 
instead  of  the  lower  bend,  the  action  will  be  essentially  the  same, 
but  the  effect  of  the  arrival  of  a  wave  train  will  be  to  decrease 
momentarily  the  plate  current  instead  of  to  increase  it.  As  before, 
there  will  be  fluctuations  of  the  plate  current  keeping  time  with  the 
arrival  of  wave  trains,  and  a  sound  in  the  telephone  of  a  pitch  cor- 
responding to  the  number  of  wave  trains  per  second. 

Care  must  be  taken  in  the  use  of  receiving  tubes  that  the  B  battery 
voltage  is  never  high  enough  to  cause  the  visible  "blue  glow"  re- 
ferred to  in  Section  184.  The  tube  becomes  very  erratic  in  behavior, 
when  in  this  condition,  and  is  very  uncertain  and  is  not  sensitive 
as  a  receiver.  This  is  because  the  plate  current  becomes  so  large 
that  it  is  unaffected  by  variations  of  the  grid  voltage.  Characteristic 
curves  will  not  repeat  themselves  if  the  tube  shows  the  blue  glow 
and  sharp  breaks  may  appear  in  any  or  all  of  the  curves.  Further- 
more the  tube  gets  hot  and  its  safety  is  endangered  by  the  blue  glow 
discharge. 

Condenser  in  Grid  Lead. — If  the  circuit  of  Fig.  253  is  used,  having 
a  condenser  in  series  with  the  grid,  the  action  of  the  tube  as  a  detector 
is  different.  It  now  depends  upon  the  form  of  the  grid  voltage — 
grid  current  curve  (dotted  curve  of  Fig.  248).  When  the  grid  voltage 
is  the  same  as  that  of  the  filament  and  there  are  no  grid  oscillations, 
Fig.  248  indicates  that  under  these  conditions  the  grid  current  is  zero; 
that  is,  no  electrons  are  passing  from  filament  to  grid.  Now  suppose 


324 


RADIO    COMMUNICATION. 


that  a  series  of  wave  trains  falls  upon  the  antenna  of  Fig.  253  as  shown 
in  (1)  of  Fig.  254.  If  the  circuit  LQ  is  tuned  to  the  same  wave  length 
as  the  antenna  circuit,  oscillations  will  bo  set  up  in  it,  and  similar 


Fia-254 


•=•      Vacuum  tube  as  deiector  of  damped 
oscillations.  Condenser  in  g-id  circuit 


I 


^'tp" — F 
®1 


Qr.J   Voltage 

rlQ.ZSj     Effect  of    S^rvili    received 
byd  VAcuutntob*  ot>on  the   t»Ut«. 
current 


FlQ.254-       Recejatlon    witn 

Grid    condenser 

<0  Incomini  oscilletlona  (z)Qn'd  Currant 
(»)Gn'd  bSWutl    W)  Plate  current 
(5j  Current  in  tel«^hon«s. 


Aeii'orv    of  A  VACOUIT\  tob« 
As    an  AmJDli'fier 


Qrid   Voltage 


voltage  oscillations  will  be  communicated  to  the  grid  by  means  of  the 
stopping  condenser  C2.1     Each  time  the  grid  becomes  positive,  elec- 


1 A  suitable  value  for  the  capacitance  of  the  condenser  Cz  is  about  0.0001  mfd. 


RADIO    COMMUNICATION.  325 

trons  will  flow  to  it,  but  during  the  negative  half  of  each  oscillation 
no  appreciable  grid  current  will  flow.  This  is  shown  in  curve  (2)  of 
Fig.  254.  Thus  during  each  wave  train  the  grid  will  continue  gain- 
ing negative  charge  and  its  average  potential  will  fall  as  shown  in  (3) 
of  the  same  figure.  This  negative  charge  on  the  grid  opposes  the 
flow  of  electrons  from  filament  to  plate,  causing  on  the  whole,  a 
decrease  in  the  plate  current.  At  the  end  of  each  wave  train  this 
charge  leaks  off  through  either  the  condenser  or  the  walls  of  the  tube 
(or  both),  and  the  plate  current  rises  again  to  its  normal  value  as 
shown  in  (4)  of  the  same  figure.  This  should  happen  before  the  next 
wave  train  comes  along,  but  sometimes  the  leak  is  not  fast  enough 
for  this  discharge  to  take  place.  In  this  case  a  better  result  is 
secured  if  a  resistance  of  a  megohm  or  so  is  shunted  across  the  con- 
denser. Such  a  resistance  is  called  a  ''grid  leak. " 

The  telephone  diaphragm  cannot  viebrate  at  radio  frequency  but 
the  high  inductance  of  its  coils  smooths  out  the  plate  current  varia- 
tions into  some  such  form  as  is  shown  at  (5)  in  the  figure.  Thus  as  in 
the  case  of  the  circuit  of  Fig.  251,  the  note  heard  in  the  telephone 
corresponds  in  pitch  with  the  frequency  of  the  wave  trains.  If  the 
waves  falling  upon  the  antenna  are  undamped  waves  they  may  be 
detected  using  either  of  these  circuits,  if  they  are  first  divided  off 
into  audio  frequency  groups.  (For  methods  see  Chapter  7,  Section 
178).  To  receive  undamped  waves  which  are  not  divided  up  into 
groups  of  audible  frequency,  vacuum  tubes  may  be  used  in  special 
ways  called  the  heterodyne  and  autodyne  methods.  See  Section 
201  below. 

192.  Effect  of  Incoming  Signals  upon  the  Plate  Current. — The 
theory  of  detector  action  just  given  involves  a  change  in  both  the 
plate  current  and  grid  current  of  the  receiving  tube.  It  is  easily 
shown  experimentally  that  such  changes  take  place.  The  result  of 
one  such  experiment  is  shown  in  Fig.  255.  The  solid  line  curve  i& 
similar  to  those  of  Fig.  248  and  shows  for  a  particular  tube  with  a 
constant  plate  voltage  the  values  of  plate  current  for  various  values 
of  grid  voltage  between  —5.5  and  +5.5  volts.  The  lower  (dotted) 
curve  shows  how  much  the  plate  current  changed  when  a  signal 
was  being  received.  The  circuit  was  so  arranged  that  the  effect 
of  the  signal  was  to  add  a  high-frequency  oscillating  voltage 
to  the  adjustable  steady  voltage  applied  to  the  grid,  as  ex- 
plained in  Section  191.  The  height  of  the  dotted  curve  shows,  for 


326  RADIO   COMMUNICATION. 

each  value  of  grid  voltage,  how  much  the  plate  current  was  changed 
by  the  signal.  It  will  be  noted  that  in  some  cases  the  effect  is  an 
increase  of  plate  current,  but  in  other  cases  a  decrease  corresponding 
to  the  different  parts  of  the  plate  current  curve,  as  explained  in  Sec- 
tion 189.  Thus  when  the  steady  voltage  applied  was  +1.1  volts, 
the  plate  current  was  increased  by  about  35  microamp.,  and  when 
the  voltage  was  zero,  by  70  microamp.  With  +1.3  volts  applied 
there  was  no  change  at  all  in  the  plate  current  when  the  signal  came 
in,  while  for  +5  volts  there  was  a  decrease  of  more  than  100  micro- 
amp,  produced  by  the  same  strength  of  signal.  Since  it  is  the  plate 
current  that  passes  through  the  telephone  receiver  it  is  evident  that 
with  this  particular  tube  the  signals  received  are  clearest  with  zero 
or  about  5  volts  positive  applied  to  the  grid,  but  1  to  1.5  volts  should 
be  particularly  avoided.  Different  tubes  show  similar  results  but 
the  voltage  values  differ  somewhat. 

The  tubes  generally  supplied  to  the  Signal  Corps  for  receiving 
(types  VT-1,  VT-11  and  VT-21)  are  all  so  designed  that  they  operate 
to  good  advantage — like  the  tube  considered  above — when  the  grid 
is  kept  at  the  same  voltage  as  the  negative  end  of  the  filament,  that 
is,  grid  voltage  zero. 

C.  The  Vacuum  Tube  as  an  Amplifier. 

193.  General  Principle. — It  was  shown  in  Section  191  that  a  vac- 
uum tube  acts  as  a  detector  or  rectifier  because  an  alternating  volt- 
age applied  to  the  grid  circuit  can  be  made  to  produce  unsymmetri- 
cal  oscillations  in  the  plate  circuit.  While  the  tube  is  thus  acting 
as  a  detector,  it  is  also  as  a  matter  of  fact  acting  as  an  amplifier.  That 
is,  greater  oscillations  are  produced  in  the  plate  circuit  for  a  given 
alternating  voltage  in  the  grid  circuit  than  would  be  produced  by 
the  same  voltage  directly  in  the  plate  circuit.  This  explains  why 
the  vacuum  tube  is  a  more  sensitive  detector  than  the  crystal  detec- 
tor, which  acts  as  a  rectifier  only. 

It  is  sometimes  desired  to  amplify  an  alternating  current  without 
any  rectifying  or  detecting  action.  This  is  done  by  keeping  a  voltage 
on  the  grid  of  such  value  that  the  symmetry  of  the  oscillations  in 
the  plate  circuit  is  not  altered.  Thus  if  there  is  a  steady  voltage 
applied  on  the  grid  of  such  value  that  the  plate  current  is  on  the  part 
of  the  characteristic  curve  that  is  practically  straight  (as  point  P 
in  Fig.  256)  then  a  small  change  in  grid  voltage  in  either  direction 
causes  the  plate  current  to  increase  or  decrease  by  the  same  amount. 


RADIO   COMMUNICATION.  327 

For  instance,  if  the  grid  voltage  is  increased  from  v  to  wt  (Fig.  256) 
or  decreased  by  an  equal  amount  from  v  to  u,  the  current  will,  in  the 
first  case,  increase  from  a  to  c  and  in  the  second  fall  off  by  an  equal 
amount,  from  a  to  b.  In  other  words  the  wave  form  of  the  grid 
voltage  variation  will  be  repeated  in  the  fluctuating  plate  cur- 
rent. The  latter  will  now  be  equivalent  to  an  alternating  current 
superinposed  upon  the  steady  plate  current  from  the  B  battery. 
The  magnitude  of  the  alternating  current  part  of  the  plate  current 
will  be  greater,  the  steeper  the  slope  of  the  curve  at  the  point  P. 

The  power  expanded  in  maintaining  the  oscillations  in  the  grid 
current  is  far  less  than  that  involved  in  the  corresponding  plate 
current  change,  because  the  grid  current  is  much  smaller  than  the 
plate  current  and  the  voltage  is  also  less.  For  example,  referring 
to  the  vacuum  tube  whose  characteristic  curves  are  given  in  Fig. 
248,  if  the  grid  voltage  oscillates  so  that  the  plate  current  fluctuates 
between  the  values  a  and  b,  the  grid  current  changes  from  about  1  to  2 
microamp.,  average  voltage  2.2  volts.  The  corresponding  change  in 
plate  current  is  from  300  to  400  microamp.,  with  average  voltage 
perhaps  35  volts.  Remembering  that  amperes  X  volts  =  watts,  we 
have  in  the  grid  circuit  a  power  expenditure  of  2.2  microwatts  and 
in  the  plate  circuit  a  corresponding  power  change  of  3500  microwatts. 
This  much  increased  power  is  drawn  from  the  energy  stored  in  the  B 
battery.  The  signals  may  be  thought  of  as  exerting  a  sort  of  relay 
action  on  the  plate  circuit,  causing  magnified  power  to  be  drawn 
from  the  B  battery.  The  tube  is  said  in  this  case  to  act  as  an  "am- 
plifier." The  variations  of  current  in  the  grid  circuit  have  been 
compared  to  the  slide  valve  of  an  engine  since  they  admit  energy 
from  the  battery  into  the  plate  circuit,  much  as  the  slide  valve 
admits  heat  energy  into  the  cylinder  of  the  engine. 

To  utilize  the  amplified  alternating  current  in  the  plate  circuit, 
the  primary  of  a  transformer  T  (Fig.  257),  may  be  placed  in  the  plate 
circuit.  From  the  secondary  of  this  transformer,  the  alternating 
current  (see  Section  60)  is  delivered  to  a  crystal  detector  or  other 
receiver;  or,  if  further  amplification  is  desirable,  to  the  grid  circuit 
of  a  second  amplifing  tube,  as  shown  in  Fig.  257.  From  this  second 
tube  it  then  goes  to  a  receiving  tube  or  crystal.  This  method  of  using 
two  or  more  tubes  for  amplification  is  called  cascade  amplification. 

Instead  of  passing  on  the  amplified  energy  by  means  of  a  trans- 
former coupling,  the  coupling  may  be  simply  a  resistance  or  a  react- 
ance. An  example  of  this  is  shown  in  Fig.  258  where  a  crystal 


328 


RADIO    COMMUNICATION. 


detector  is  shown  as  the  receiver.  To  get  the  greatest  power  output 
from  the  tube  a  resistance  should  be  used  in  the  plate  circuit  of  a 
value  equal  to  the  average  internal  resistance  of  the  tube,  just  as 
in  the  case  of  a  direct  current  generator  of  constant  voltage,  the  great- 


est  power  output  occurs  when  the  internal  resistance  equals  the 
external. 

194.  Elementary    Theory    of    Amplification. — The    characteristic 
curves  of  a  vacuum  tube  show  that  an  increase  in  the  grid  voltage 


RADIO   COMMUNICATION.  329 

makes  a  much  greater  increase  in  the  plate  current  than  the  same  in- 
crease in  the  plate  voltage  itself  would  do.  Consider,  for  instance,  the 
two  upper  curves  of  Fig.  248,  p.  318.  From  the  curve  marked  "30 
volts"  we  see  that  the  plate  current  increases  from  200  to  400  micro- 
amp,  when  the  grid  voltage  is  increased  from  1.2  to  3  volts,  or  110 
microamp.  per  volt  change.  If  on  the  other  hand,  the  grid  voltage  is 
left  unchanged  at  1.2  volts  and  the  plate  voltage  increased  to  35  volts, 
the  upper  curve  shows  that  the  plate  current  increases  to  280  micro- 
amp.;  a  change  of  80,  or  16  microamp.  for  each  volt.  In  other 
words  a  volt  added  to  the  grid  voltage  makes  about  7  times  as  much 
change  in  the  plate  current  as  a  volt  added  to  the  plate  voltage 
would  make.  This  number  which  represents  the  relative  effects  of 
grid  voltage  and  plate  voltage  upon  plate  current  is  called  the  "am- 
plification constant"  of  the  tube.1  The  greater  this  amplification 
constant  is,  the  more  efficient  is  the  tube  as  an  amplifier  of  weak 
signals.  It  may  be  defined  as  the  ratio  of  the  change  in  plate  current 
per  volt  on  the  grid  to  the  change  in  plate  current  per  volt  on  the 
plate. 

The  two  principal  constants  of  a  tube  are  the  amplification  con- 
stant just  defined  and  the  internal  resistance.  The  latter  is  the 
resistance  to  an  alternating  current  between  plate  and  filament  in 
the  tube.  These  two  constants  may  be  calculated  from  the  char- 
acteristic curves  of  the  tube,  or  may  be  measured  by  a  simple  method 
like  a  bridge  measurement.2  The  voltage  amplification  given  by 
an  amplifying  circuit  may  be  calculated  from  these  two  constants 
of  the  vacuum  tube. 

The  voltage  amplification  may  be  defined  as  the  ratio  of  the  voltage 
change  produced  in  the  output  apparatus  in  the  plate  circuit  to 
the  change  in  the  voltage  impressed  on  the  grid.  Thus  in  the  re- 
sistance coupled  amplifier,  of  Fig.  258,  it  is  the  ratio  of  the  voltage 
between  of  and  V  at  the  terminals  of  R  to  the  voltage  applied  be- 
tween a  and  b .  Calling  the  amplification  constant  K  and  the  internal 
resistance  R0,  it  can  be  shown  that  the  voltage  amplification  for  such 
an  amplifier  is 

KR 

R+R0' 

1  The  theory  of  amplification  has  been  worked  out  in  more  detail  by  Langmuir, 
Proc.  Inst.  Radio  Engineers,  3,  p.  261,  1915;  by  Vallauri,  L'Elettrotecnica,  3,  p. 
43,  1917;  and  by  H.  J.  Van  der  BijI,  Physical  Review,  12,  p.  171,  1918. 

2  For  information  on  such  measurements  see  papers,  by  J.  M.  Miller,  Proceedings 
Institute  of  Radio  Engineers,  6,  p.  141, 1918;  and  H.  J.  Van  der  Bijl,  Physical  Review, 
12,  p.  171,  1918. 


330  RADIO   COMMUNICATION. 

195.  Audio  Frequency  Amplification. — In  the  preceding  discussion 
of  amplification,  it  was  pointed  out  that  after  a  radio  frequency  cur- 
rent is  amplified  it  is  passed  through  some  rectifying  device.     This 
latter  is  not  necessary  when  an  audio  frequency  current  is  amplified, 
for  the  amplified  current  can  be  received  with  a  telephone  receiver 
placed  in  the  plate  circuit  of  the  amplifier.     It  is  sometimes  desired 
to  amplify  the  audio  frequency  current  produced  in  a  radio  rectifying 
device.     In  this  case  the  radio  current  consisting  of  groups  of  oscil- 
lations is  first  passed  into  the  rectifying  device,  and  the  pulses  of 
current  having  the  group  frequency  are  passed  on  into  the  ampli- 
fier.   The  amplifying  process  may  be  carried  on  through  several 
steps,  as  in  cascade  amplification  shown  in  Fig.  257.    An  amplifier 
consisting  of  two  type  VT-1  tubes  in  cascade  is  said  to  give  an  ampli- 
fication of  10,000  times. 

196.  Regenerative  Amplification. — It  is  possible  to  increase  the 
sensitiveness  of  a  vacuum  tube  as  a  detector  enormously  by  a  method 
which  makes  use  of  its  amplifying  action.1    The  connections  are 
shown  in  Fig.  259.     The  explanation  of  the  amplifying  action  is  as 
follows.   Oscillations  in  the  circuit  LL2C,  applied  to  the  grid  through 
the  condenser  C1,  produce  corresponding  variations  in  the  continu- 
ous plate  current,  the  energy  of  which  is  supplied  by  the  battery  B. 
This  plate  current  flows  through  L3  and  by  means  of  the  mutual 
inductance  M,  some  of  the  energy  of  the  plate  oscillations  is  trans- 
ferred back  to  the  grid  circuit,  and  the  current  in  the  circuit  LL2  C 
is  thus  increased.     This  produces  amplified  grid  oscillations  which, 
by  means  of  the  grid,  produce  larger  variations  in  the  plate  current, 
thus  still  further  reinforcing  the  oscillations  of  the  system.     Simul- 
taneously with  this  amplification  the  regular  detecting  action  goes 
on;  the  condenser  Cl  is  charged  in  the  usual  way,  but  accumulates  a 
charge  which  is  proportional,  not  to  the  original  signal  strength, 
but  to  the  final  amplitude  of  the  oscillations  in  the  grid  circuit. 
The  result  is  a  current  in  the  telephone  much  greater  than  would  have 
been  obtained  from  the  original  oscillations  in  the  circuit. 

To  obtain  maximum  voltage  on  the  grid,  the  circuit  LL2C  should 
have  large  inductance  and  small  capacity.  The  connection  between 
L2  and  L3  must  be  so  made  that  their  mutual  inductance  is  of  proper 
sign  to  produce  an  emf.  which  will  aid  the  oscillations  instead  of 
opposing  them.  Various  modifications  of  this  method  are  used. 

i  This  is  due  to  E.  H.  Armstrong  and  is  described  by  him  in  Proceedings  Insti- 
tute of  Radio  Engineers,  3,  p.  215, 1915. 


RADIO   COMMUNICATION. 


331 


The  condenser  C  may  be  across  L3,  so  that  the  tuned  oscillatory  cir- 
cuit is  in  series  with  the  plate  instead  of  the  grid.  Or,  C  may  be 
connected  across  all  of  the  inductance  in  series,  the  oscillation 
circuit  then  including  L,  L2,  and  L3. 

Combination  Radio  and  Audio  Regenerative  Amplification. — A  sin- 
gle vacuum  tube  can  be  used  to  amplify  and  detect  radio  frequency 
current  and  simultaneously  amplify  the  telephone  pulses  of  audio 
frequency.  The  circuits  are  shown  in  Fig.  260.  Here  M2  repre- 
sents the  coupling  for  the  radio  frequency,  and  the  coils  are  of  rela- 
tively small  inductance.  M3  is  the  coupling  for  the  audio  frequency, 
and  the  transformer  is  made  up  of  coils  having  an  inductance  cf  a 


Comb'mat.o*  of  Vacuum 
tub*  amblifiWr  And  crystal 
detecto 


henry  or  more.  The  variable  condensers  C3  and  C4  have  the  double 
purpose  of  tuning  M3  to  the  audio  frequency  and  of  by-passing  the 
radio  frequencies.  The  radio  frequency  variations  in  the  plate  cur- 
rent flow  through  the  circuit  PFL3C4C5L4  and  at  the  same  time  the 
audiofrequency  variations  flow  through  PFL3LQTBL^.  The  total 
amplification  of  weak  signals  by  this  method  is  about  100  times 
that  of  the  ordinary  audion  bulb.  On  stronger  signals  the  amplifi- 
cation is  smaller. 

197.  Vacuum  Tube  Amplifier  with  Crystal  Detector. — The  charac- 
teristic curves  of  a  vacuum  tube  show  that  the  best  value  of  grid 
voltage  for  amplification  is  not  the  same  as  for  best  detecting  action, 


332  RADIO   COMMUNICATION. 

which  is  an  argument  for  using  separate  tubes  for  these  two  purposes. 
This  adds  somewhat  to  the  complexity  of  the  apparatus,  and  leads 
some  operators  to  prefer  the  combination  of  a  vacuum  tube  for  am- 
plifying and  a  crystal  detector  for  receiving.1  Such  a  circuit  is 
shown  in  Fig.  261. 

The  oscillating  circuit  L  C  is  coupled  to  the  antenna  and  is  tuned 
to  the  frequency  of  the  latter,  which  is  that  of  the  incoming  waves. 
The  alternations  of  voltage  between  the  terminals  of  the  coil  L  are 
applied  between  the  filament  F  and  grid  G  through  the  battery  6, 
which  has  been  previously  adjusted  in  voltage  so  that  the  plate  cur- 
rent has  a  value  corresponding  to  a  point  on  the  straight  part  of  its 
characteristic. 

The  amplified  oscillations  in  the  plate  circuit  are  communicated 
to  the  oscillating  circuit  L^C^  which  is  coupled  to  the  plate  circuit 
through  the  coil  M.  The  circuit  LlCl  is  tuned  to  the  frequency  of 
the  received  waves  like  the  other  two  circuits.  The  alternations  of 
voltage  between  the  terminals  of  the  coil  L^  are  rectified  in  the  crys- 
tal detector  D  in  the  usual  way,  and  cause  an  audio  frequency  cur- 
rent to  flow  in  the  telephone  receivers. 

D.  The  Vacuum  Tube  as  a  Generator. 

198.  Conditions  for  Oscillation. — The  vacuum  tube  can  be  made 
to  generate  high  frequency  currents,  and  thus  act  as  a  source  of 
radio  current  for  the  transmission  of  signals  or  other  purposes.  The 
principle  may  be  illustrated  by  Fig.  259.  As  explained  previously, 
the  coupling  M  between  the  coils  L2  and  L3  transfers  some  of  the 
power  in  the  plate  circuit  back  to  the  grid  circuit,  thus  greatly 
increasing  the  original  voltage  on  the  grid.  If  the  coupling  is  made 
so  close  that  the  voltage  fed  back  to  the  grid  circuit  is  greater  than 
the  voltage  originally  there,  the  oscillation  will  continue  even  though 
the  original  source  which  caused  the  oscillation  is  removed.  Con- 
tinuous or  undamped  oscillations  may  be  generated  by  a  vacuum 
tube  used  thus  as  an  "oscillator"  of  any  frequency  between  one 
per  second  and  10,000,000  per  second.2 

A  great  variety  of  circuits  have  been  used  for  generating  oscilla- 
tions by  means  of  vacuum  tubes.  A  simple  and  practical  circuit 

1  G.  Martinez,  L'Elettrotecnica,  4,  p.  278,  1917. 

2  "The  Pliotron  Oscillator  for  Extreme  Frequencies."— W.  C.  White,  G.  E.  Re- 
view, 19,  p.  771, 1916. 


RADIO    COMMUNICATION. 


333 


for  the  purpose  is  shown  in  Fig.  262.  The  inductance  Z3  and  the 
capacitance  C  are  given  values  that  will  produce  the  frequency 
desired.  Any  electrical  disturbance  may  start  oscillations  in  L3C, 
for  example,  the  slight  rush  of  current  produced  by  closing  the 
battery  circuit  or  changing  the  value  of  C.  By  means  of  the  coup- 
ling M,  this  applies  a  voltage  to  the  grid.  The  grid  then  amplifies 
the  oscillations  in  the  plate  circuit,  and  by  means  of  the  coupling  M 
a  still  larger  oscillating  voltage  is  impressed  upon  the  grid.  This  is 
often  spoken  of  as  a  "feed  back"  action.  If  L2,  L3,  C,  and  the 
resistance  of  the  circuit  L3C  have  suitable  values,  oscillations  are 
produced  in  the  circuit  and  are  built  up  to  some  final  value  as 
shown  in  Fig.  263.  At  the  upper  left  corner  of  the  figure  is  shown 
the  plate  current-grid  voltage  characteristic  curve  of  the  tube; 


PlG.ZfeZ 


Use  of  Vacaum  tube  AS 
osoilldtlcm    Generator 


below  is  shown  the  building  up  of  the  grid  voltage  oscillations,  and 
to  the  right  the  growth  of  the  oscillations  in  the  plate  current. 
After  a  time  a  limit  is  reached  in  the  magnitude  of  oscillations. 
This  limit  may  correspond  with  an  oscillation  amplitude  reaching 
from  one  bend  of  the  characteristic  curve  to  the  other.  Any  further 
increase  in  grid  voltage  oscillations  produces  little  further  increase 
in  plate  current.  This  is  shown  by  the  flattening  out  of  the  char- 
acteristic curve  at  each  end. 

The  readiness  of  a  tube  to  oscillate  depends  upon  the  slope  of 
the  characteristic  curve  (Fig.  263)  and  the  internal  resistance  of  the 
tube.  If  the  curve  has  a  steep  slope,  it  means  that  a  small  change 
in  grid  voltage  will  cause  a  large  change  in  plate  current.  Such  a 


334  RADIO   COMMUNICATION. 

tube  is  sensitive  and  oscillates  readily.  In  order  that  the  tube 
may  oscillate  at  all,  the  coupling  between  L2  and  L3  must  be  closer 
than  a  certain  value.  Mathematical  analysis  shows  that  in  general 
grid  and  plate  should  be  of  opposite  potential,  with  respect  to  the 
filament,  and  that  grid  voltage  should  be  small  compared  with 
plate  voltage.  Thus  the  type  VT-2  tube  used  by  the  Signal  Corps 
as  a  generator,  normally  operates  with  a  plate  voltage  of  +300  and 
a  grid  voltage  of  —20,  while  the  receiving  and  amplifying  tube 
type  VT-1  has  a  plate  voltage  of  +20  and  a  grid  voltage  of  zero.1 

199.  Practical  Considerations  in  Using  Vacuum  Tubes  as  Oscilla- 
tion Generators. — It  is  necessary  to  connect  the  terminals  of  the  coil 
in  the  grid  circuit  (L2in  Fig.  262)  by  trial  in  such  direction  as  to 
assist  rather  than  oppose  the  oscillations  in  the  plate  circuit  coil. 
The  two  coils  L2  and  L3  may  be  conveniently  wound,  end  to  end, 
on  the  same  supporting  core.  With  given  coils,  as  the  capacitance 
is  increased,  there  comes  a  point  where  the  oscillation  current 
breaks  or  falls  off  to  zero.  It  is  then  necessary  to  use  coils  of  greater 
inductance  to  obtain  longer  wave  lengths. 

The  vacuum  tube  is  far  superior  to  the  buz;aer  as  a  source  of  oscil- 
lations for  measurement  purposes.  To  secure  constancy  in  both 
amplitude  and  frequency,  it  is  desirable  where  several  tubes  are 
used  in  the  same  circuit,  to  have  separate  batteries  for  each  tube. 
With  care  in  this  regard,  constancy  in  both  amplitude  and  frequency 
may  be  secured  tto  one-tenth  of  one  per  cent. 

A  circuit  suitable  for  producing  oscillations  and  transferring  their 
power  to  a  radiating  antenna  is  shown  in  Fig.  264.  Here  the  coup- 
ling between  grid  and  plate  circuits  is  secured  by  means  of  two 
inductances,  L^  and  L2  connected  in  series  in  the  antenna  circuit. 
These  are  inductively  connected,  the  one  to  L3  in  the  grid  circuit 
and  the  other  to  L4  in  the  plate  circuit.  One  or  the  other  is  vari- 
able. See  also  circuits  given  below  in  Radio  Telephony. 

The  coupling  between  grid  and  plate  circuits  needed  for  securing 
oscillations  in  a  tube  need  not  be  inductive;  capacitive  coupling 
may  be  used.  One  such  circuit  is  given  in  Fig.  265.  Condenser  C2 
provides  the  coupling.  Inductances  Ll  and  L2  are  variable  and 
approximately  equal.  C/is  a  fixed  condenser  which  serves  as  a 
by-pass  for  the  high  frequency  current  around  the  battery.  The 
frequency  is  determined  mainly  by  values  of  Llt  L2  and  C2. 

1  A  fuller  discussion  of  the  conditions  for  generating  oscillations  in  a  tube  may  be 
found  in  a  paper  by  L.  A.  Hazeltine  in  Proceedings  Institute  of  Radio  Engineers, 
6,  p.  63,  1918. 


RADIO    COMMUNICATION. 


335 


200.  Tubes  Suitable  for  Developing  Considerable  Power. — The 
output  of  the  vacuum  tube  as  a  generator  cannot  be  large  unless  the 
tube  has  a  vacuum  sufficiently  good  to  permit  a  large  B  battery 
voltage;  this  is  because  the  power  output  cannot  exceed  the  pro- 
duct of  plate  current  and  plate  voltage.  For  example,  the  type 
VT-14  tube,  supplied  by  the  Signal  Corps  as  an  oscillation  generator., 
is  operated  with  about  350  volts  on  the  plate  and  has  a  power  out- 


Control    of  Antenna   torrent  m   radi'o 
•J-e-lefahony   by  vac.o»om  Tub«  modulator 


put  of  about  3  watts.  Large  pliotrons  (see  Fig.  250)  are  capable 
of  developing  very  much  more  power  because  they  are  able  to  stand 
several  thousand  volts  on  the  plate  and  also  carry  a  plate  current 
as  high  as  400  milliamp.  Ability  to  stand  a  high  voltage  in  the 
plate  circuit  depends  principally  upon  the  use  of  a  very  high  vacuum. 
Ability  to  carry  a  large  plate  current  varies  with  the  size  of  the  tube 
and  the  facilities  for  getting  rid  of  the  heat  developed.  Thus  the 


336  RADIO    COMMUNICATION. 

power  output  of  a  single  large  tube  may  be  as  high  as  a  kilowatt, 
and  since  a  number  of  such  tubes  can  be  operated  in  parallel,  a  large 
amount  of  power  can  be  handled.  In  the  long  distance  radio  tele- 
phone experiments  between  Arlington,  Va.,  and  Hawaii  in  1916,  the 
power  supplied  to  the  Arlington  antenna,  amounting  to  9  kilowatts, 
was  furnished  by  a  large  number  of  generator  tubes  operating  in 
parallel,  each  with  600  volts  on  its  plate.  The  antenna  current  was 
60  amp. 

201.  Heterodyne  and  Autodyne  Receiving  by  Vacuum  Tubes. — If 
two  tuning  forks  mounted  on  resonance  boxes,  one  vibrating  256  and 
the  other  260  times  per  second  are  sounding  together,  a  listener  a 
short  distance  away  will  hear  a  sound  alternately  swelling  out  and 
dying  away  four  times  per  second.  These  tone  variations  are  called 
''beats."  Similarly,  if  two  sources  of  undamped  electrical  oscilla- 
tions act  simultaneously  upon  the  same  circuit,  one  of  frequency 
500,000  and  the  other  of  501,000,  the  amplitude  of  the  combined 
oscillation  will  successively  rise  to  a  maximum  and  fall  to  a  minimum 
1000  times  per  second.  If  rectified  by  a  vacuum  tube  or  a  crystal, 
their  variations  will  produce  an  audible  note  of  frequency  1000  in  a 
suitable  receiving  telephone.  If  one  of  the  two  oscillations  is  the 
received  signal  in  the  antenna  and  the  other  is  generated  by  a  circuit 
in  the  receiving  station,  we  have  ''heterodyne"  or  "beat"  recep- 
tion. In  the  receiving  telephone,  a  musical  note  is  heard,  the  pitch 
of  which  is  readily  varied  by  slight  variation  of  tuning  of  the  local 
generating  circuit. 

If  a  regenerative  circuit  similar  to  that  of  Fig.  259,  p.  328,  is  used  (L 
being  coupled  to  the  antenna),  the  same  tube  may  be  used  as  a  detector 
and  as  a  generator  of  local  oscillations.  This  is  called  "autodyne" 
reception.1  The  procedure  is  to  tune  the  antenna  circuit  to  the 
incoming  signals  and  adjust  the  local  oscillating  circuit  so  that  it  is 
slightly  out  of  tune  with  the  incoming  signals.  Thus  beats  of  audible 
frequency  are  produced.  Measurements  have  shown  that  this 
method  is  so  sensitive  that  signals  can  be  heard  when  the  power 

received  is  equal  to  only  y^y-5  watt. 

By  these  methods  of  reception  very  faint  signals  can  be  received. 
Also  interference  from  other  stations  is  reduced  to  a  minimum, 

1  A  detailed  explanation  of  autodyne  receiving  is  given  in  C.  74,  p.  215.  For  further 
information  see  also  articles  by  L.  De  Forest,  Electrical  World,  65,  p.  465,  1915; 
E.  H.  Armstrong,  Proceedings  Institute  of  Radio  Engineers,  3,  p.  215,  1915:  4,  p.  204, 
1916;  G.  Vallauri,  L'Elettrotecnica  3,  p.  43,  1917. 


RADIO   COMMUNICATION. 


337 


because  a  slight  difference  in  frequency  of  the  interfering  signal  would 
give  a  note  of  entirely  different  pitch,  or  even  inaudible.  For  in- 
stance, if  the  local  oscillation  had  a  frequency  of  500,000  (X=600 
meters),  the  received  oscillation  501,000  and  the  interfering  oscilla- 
tion 502,000,  the  interfering  note  would  have  the  frequency  2000, 
or  be  a  whole  octave  higher  in  pitch  than  the  received  note.  If  the 
interfering  source  had  a  frequency  530,000,  its  beat  tone  would  be 
so  high  as  to  be  entirely  inaudible. 

E.  Radio  Telephony. 

202.  Voice  Modulation  of  Radio  Currents  by  Vacuum  Tubes. — The 
principles  of  radio  telephony  are  the  same  as  those  of  radio  telegraphy 


FloctbalYon-s   in  Cjrid  Volfage 


t?.  Varying  amplitude  of  oscillations   " 
Anfermfc 

Voice    Modulatt'orx?    of   J\nfer\rva 

O*cf  Hat  fort? 


by  undamped  waves  except  that  the  sending  key  is  replaced  by 
apparatus  which  varies  the  sending  current  in  accordance  with  the 
sound  waves  produced  by  the  voice.  A  wave  of  radio  frequency  is 
sent  out  by  the  antenna,  the  intensity  of  which  varies  with  the  fre- 
quency of  the  voice  sound  waves.  The  sound  waves  have  a  fre- 
quency much  lower  than  the  radio  frequency,  so  that  each  sound 
wave  lasts  over  a  considerable  number  of  radio  alternations,  as  in 
the  lower  curve  of  Fig.  267.  The  radio  wave  is  thus  transmitted  in 
97340° — 19 22 


338  RADIO    COMMUNICATION. 

pulses,  and  is  received  on  any  ordinary  apparatus  used  for  receiving 
damped  wave  radio  telegraphic  signals. 

The  power  involved  in  the  sound  waves  generated  in  ordinary 
speech  is  relatively  very  small,  perhaps  0.00000001  watt,  yet  this 
must  he  made  to  control  a  kilowatt  or  more  of  radio  frequency  power 
in  long  distance  radio  telephony.  The  effect  of  the  sound  waves 
must  therefore  he  amplified.  The  way  in  which  the  audio  fre- 
quency is  made  to  control  the  amplitude  of  the  radio  oscillation  will 
now  be  explained. 

Suppose  a  generator  of  radio  oscillations  is  placed  in  series  with  the 
antenna,  as  in  Fig.  266.  Various  types  of  arc,  quenched  spark, 
timed  spark,  high  frequency  alternators,  and  vacuum  tube  oscil- 
lators have  all  been  used  as  sources  with  some  success.  The  con- 
trolling device  is  usually  the  combination  of  a  telephone  transmitter 
with  an  arrangement  of  vacuum  tube  circuits,  as  shown  in  Fig. 
266.  The  plate  circuit  of  the  vacuum  tube  is  inductively  coupled 
to  the  antenna  by  the  coil  L.  The  grid  of  the  tube  is  kept  at  a  nega- 
tive voltage  by  the  battery  C.  The  current  through  the  antenna 
coil  induces  potential  differences  between  filament  and  plate,  but 
this  produces  only  very  slight  changes  in  plate  current  on  account 
of  the  large  negative  voltage  of  the  grid.  Now  suppose  voltage 
variations  of  audio  frequency  are  impressed  on  the  grid  by  means 
of  the  telephone  transmitter  Tand  the  transformer  Tr.  As  the  grid 
becomes  less  negative  or  even  somewhat  positive,  the  rectified  plate 
current  increases,  absorbing  power  from  the  antenna  and  diminish- 
ing the  amplitude  of  the  antenna  oscillations.  The  high  frequency 
oscillations  in  the  antenna  therefore  show  variations  in  amplitude 
which  keep  time  with  the  audio  frequency  variations  of  voltage  in 
the  grid  circuit,  diminution  of  antenna  current  corresponding  with 
increasing  positive  potential  of  grid.  These  variations  are  illus- 
trated in  Fig.  267.  In  the  upper  part  of  the  figure  the  fluctuations 
of  grid  voltage  due  to  the  telephone  transmitter  appear;  in  the  lower 
part  of  the  figure  are  shown  the  resulting  variations  in  the  amplitude 
of  the  high  frequency  oscillations  in  the  radiating  antenna. 

The  audio  frequency  variations  of  amplitude  in  the  radio  fre- 
quency wave  will  be  reproduced  in  the  antenna  of  the  receiving 
station,  and  these  will  be  rectified  in  the  receiving  circuit  giving 
in  the  telephone  receiver  audio  frequency  variations  of  current, 
corresponding  in  frequency  and  wave  form  to  the  boundary  of  the 
curve  in  the  lower  part  of  Fig.  267  (as  shown  by  the  dotted  line). 
For  another  and  perhaps  simpler  explanation  of  modulation,  see 
S.  C.  Radio  Pamphlet  No.  1,  page  46. 


RADIO   COMMUNICATION.  339 

203.  Other  Methods  of  Voice  Modulation.— The  most  striking  dem- 
onstration of  the  possibilities  of  radio  telephony  was  that  carried 
out  in  1916  when  spoken  messages  sent  out  from  Arlington,  Virginia, 
were  heard  in  Paris  and  in  Hawaii,  the  latter  a  distance  of  5100 
miles.     In    these    experiments    the    oscillations    were    generated, 
modulated  and  received  by  vacuum  tubes.     Other  methods,  how- 
ever, of  generation  and  also  of  voice  modulation,  have  met  with 
success.     Two  of  these  methods  are  mentioned  here. 

Control  by  Microphones. — The  usual  method  is  to  introduce  special 
microphones  directly  into  the  antenna  circuit.  An  ordinary  micro- 
phone transmitter  can  carry  but  0.2  amp.  of  current  involving 
power  consumption  of  only  2  watts,  without  injurious  heating.  In 
order  to  control  considerably  greater  quantities  of  power,  various 
modifications  have  been  used.  For  example,  Lorenz  used  as  many 
as  25  microphones  joined  in  parallel,  Fessenden  developed  special 
water  cooled  microphones,  Egner  and  Holmstrom  used  oil  cooling. 
Marzi  a  microphone  with  a  moving  stream  of  carbon  grains,  Chambers 
and  also  Vanni  microphones  in  which  the  varying  resistance  was 
supplied  by  a  stream  of  conducting  liquid  impinging  upon  the 
vibrating  diaphragm. 

Ferromagnetic  Control. — This  method  of  controlling  the  radiation 
of  an  antenna  by  the  voice  depends  upon  the  fact  that  the  per- 
meability of  iron  varies  with  the  intensity  of  magnetization.  (See 
Chapter  1,  Section  42.)  As  the  magnetization  increases,  the  per- 
meability rapidly  increases  to  a  maximum,  and  then  slowly  drops. 
Consequently  if  we  pass  a  gradually  increasing  current  through  an 
iron  core  solenoid,  the  inductance  of  the  coil  at  first  increases  rapidly 
and  then  decreases  slowly.  Two  systems  based  on  this  principle 
are  in  use  at  present,  one  developed  by  the  Telefunken  Co.  (Ger- 
many), the  second  by  the  General  Electric  Co.  (U.  S.  A.).  For  a 
full  discussion  of  the  circuits  employed  and  their  action,  see  A.  N. 
Goldsmith's  "Radio  Telephony"  (1918),  Chapter  8,  pp.  182-203. 

204.  Practical  Use  of  Vacuum  Tubes  in  Radio  Telephony. — An 
example  of  the  use  of  a  vacuum  tube  for  modulating  the  oscillations 
in  a  radiating  antenna  has  been  given.     In  radio  telephony  vacuum 
tubes  have  been  used  also  for  generating  the  high  frequency  oscilla- 
tions needed  as  well  as  for  modulating  them.     Oscillions,  pliotrons, 
and  other  high  power  tubes  are  well  adapted  for  such  use. 

In  the  illustration  given  (Fig.  266),  the  modulation  of  the  antenna 
current  for  radio  telephony  was  secured  by  applying  the  voltage 
variations  produced  by  a  telephone  transmitter  to  the  grid  of  the 


340  RADIO    COMMUNICATION. 

controlling  tube,  the  plate  circuit  of  the  same  tube  being  induc- 
tively coupled  to  a  radiating  antenna.  When  the  source  of  radiated 
energy  is  an  oscillating  vacuum  tube,  a  different  method  of  voice 
modulation  can  be  used.  In  the  example  cited,  the  modulating  tube 
acted  directly  upon  the  high-frequency  a.c.  output,  but  with  a 
vacuum  tube  source,  the  control  of  the  direct  current  in  the  plate 
circuit  may  accomplish  the  same  end.  An  example  of  this  method 
is  found  in  a  radio  telephone  set  developed  for  Signal  Corps  use. 
To  understand  the  operation  of  this  principle,  it  is  convenient  to 
think  of  the  effect  of  variation  of  grid  voltage  as  a  change  in  the 
resistance  between  the  plate  and  filament  of  the  tube.  Consider,  for 
instance,  the  30-volt  curve  of  Fig.  248,  p.  318.  With  3  volts  on  the 
grid,  30  volts  on  the  plate  produce  a  current  of  400  microamp.,  whereas 
with  1.4  volts  on  the  grid,  the  same  plate  voltage  produces  200 
microamp.  That  is,  there  is  effectively  a  resistance  in  the  plate 
circuit  of  75,000  ohms  in  the  first  case  and  of  150,000  ohms  in  the 
second  case.  Now  suppose  the  modulator  tube  and  the  oscillating 
tube  are  connected  together  in  parallel,  the  plate  circuit  of  each 
across  the  same  d.c.  source.  The  telephone  transmitter  is  con- 
nected to  the  primary  of  a  transformer  whose  secondary  is  connected 
to  the  grid  circuit  of  the  modulator  tube.  Thus  the  resistance  of 
the  modulator  tube  will  be  considerably  varied  by  the  voice  speaking 
into  the  transmitter,  and  the  amount  of  direct  current  passing 
through  it  will  be  subject  to  audio  frequency  changes.  Suppose  that 
the  plates  of  the  modulating  and  oscillating  tubes,  joined  in  parallel, 
are  fed  by  a  constant  current  d.c.  dynamo.  As  the  current  taken 
by  the  modulator  varies  in  response  to  the  voice  variations,  the 
amount  of  current  taken  by  the  plate  circuit  of  the  oscillating  tube- 
in  parallel  with  it  on  a  constant  cusrent  source — will  vary  inversely. 
This  scheme  is  illustrated  in  Fig.  268. 

The  telephone  transmitter  and  the  transformer  are  shown  at  T 
and  Tr.  The  modulating  and  oscillating  vacuum  tubes  are  shown 
at  M  and  0.  The  d.c.  genera  tor  shown  at  D  has  a  double  winding 
on  its  armature,  each  with  its  own  commutator.  One  supplies  275- 
volt  current  for  the  two  plate  circuits  in  parallel,  and  the  other 
lights  the  two  filaments  in  series.  The  connection  of  the  generator 
to  the  plates  is  through  the  high  inductance  coils  L2  and  L3.  These 
coils  change  the  275-volt  energy  from  a  constant  voltage  supply  to  a 
constant  current  supply,  thus  furnishing  a  constant  power  output 
which  is  divided  between  the  oscillator  and  modulator  tubes  in 


RADIO   COMMUNICATION. 


341 


accordance  with  the  control  exercised  through  the  grid  circuit  of  the 
modulator.  Type  VT-2  tubes  can  be  used  both  for  modulator  and 
oscillator. 

The  receiving  set  used  with  this  transmitter  contains  three  tubes, 
one  functioning  as  detector  and  two  as  amplifiers.  Type  YT-1 
tubes  are  suitable  for  both  purposes.  The  wide  range  of  usefulness 
of  the  vacuum  tube  in  modern  radio  practice  is  well  illustrated  in 
this  set,  whose  five  tubes  are  used  for  four  differet  purposes,  namely, 
for  generating  oscillations,  for  controlling  amplitude  of  same  by  voice 
modulation,  for  amplification,  and  for  reception. 

The  General  Electric  Co.  pliotrons  are  suitable  generator  tubes 
for  long  distance  radio  telephony.  The  vacuum  is  so  good  that  they 


Cennec/fi'on    of    rnoduUtor  And   >«n«r.aTe>r 
tubes    for  r*J.o   Telephony 


-==  E. 


can  stand  thousands  of  volts  between  plate  and  filament  without 
showing  any  blue  glow.  The  output  is  several  hundred  watts,  and 
a  number  of  such  tubes  may  be  used  together  in  parallel. 

It  appears  that  radio  telephone  sets  in  which  vacuum  tubes  are 
used  both  for  generating  and  modulating  currents  of  radio  frequency 
are  likely  to  find  use  in  military  operations  of  far  greater  importance 
than  they  have  in  the  present  war  and  they  were  beginning  to  play 
a  very  real  part  during  the  year  1918.1 


For  further  information  on  radio  telephony  see  Goldsmith's  "  Radio  Telephony." 


APPENDIX  1. 
SUGGESTED  LIST  OF  LABORATORY  EXPERIMENTS. 

Experiment  1.  Effects  Produced  by  Electric  Current. — (a)  Mag- 
netic.— Put  in  series  a  4-volt  storage  battery,  key,  3-ohm  rheostat, 
and  about  2  meters  (about  7  ft.)  of  copper  wire  of  about  1  mm.  (0.04 
in.)  diameter.  Place  a  portion  of  the  copper  wire  parallel  to  a  small 
compass  needle  and  1  cm.  (0.4  in.)  or  more  above  it.  Repeat,  with 
the  wire  just  below  the  compass  needle.  Repeat  with  battery  con- 
nection reversed.  Test  out  the  right  hand  rule  for  direction  of  cur- 
tent.  Connect  a  small  electromagnet  in  the  circuit,  and  note  be- 
havior like  a  permanent  magnet. 

(b)  Heat. — Take  electromagnet  out  of  the  circuit  and  connect  in 
about  a  half  meter  of  iron  wire  about  \  mm.  in  diameter.     Reduce 
resistance  in  rehostat  until  all  out,  and  observe  iron  wire  get  hot. 
Shorten  iron  wire  and  repeat.     Replace  iron  wire  by  a  short  piece  of 
2-amp.  fuse  wire.     Reduce  resistance  in  rheostat  until  wire  melts. 

(c)  Chemical. — Immerse  two  copper  wires  connected  to  a  battery 
in  a  vessel  containing  copper  sulphate  solution  (about  10  per  cent, 
slightly  acid).     Allow  current  to  flow  for  some  time  and  note  effect. 

Experiment  2.  Ohm's  Law. — (a)  Current  inversely  proportional  to 
resistance. — Connect  in  series  a  4-volt  storage  battery,  a  milliammeter 
(10  to  150  milliamp.)  and  a  400-ohm  rheostat.  Reduce  resistance 
by  about  8  approximately  equal  steps.  Make  list  of  corresponding 
values  of  resistance  and  current. 

(b)  Current  Proportional  to  Emf. — Connect  in  series  two  similar 
cells,  a  milliammeter,  and  about  a  40-ohm  resistor.     Note  the  cur- 
rent.    Take  out  one  cell  and  note  current  again. 
E_2E_ 
J—p-R 

Experiment  3.  Voltmeter- Ammeter  Method  of  Measuring  Resist- 
ance.— Send  enough  current  through  an  incandescent  lamp  to  make 
the  filament  bright.    Measure  current  by  ammeter  in  series,  and 
voltage  by  voltmeter    connected  across  the  lamp,   and  calculate 
342 


RADIO    COMMUNICATION.  343 

resistance.  Measure  resistance  in  this  manner  of  the  filament  of  a 
type  VT-1  or  type  VT-2  tube  taking  its  normal  current. 

Experiment  4.  Use  of  Wheatstone  Bridge. — Connect  apparatus  of 
which  resistance  is  desired  to  the  terminals  marked  X.  Press 
battery  key,  tap  galvanometer  key  lightly.  Suitable  resistances 
to  measure  are  those  of  filaments  (cold)  of  vacuum  tubes,  milliam- 
meter,  microammeter,  field  of  pack  set  generator,  sliding  contact 
rheostat. 

Experiment   5.  Series   and  Parallel  Connections. — (a)  Test  of  the 

Relation,  -5= — 1 —  or  R=    \  2  . — Apparatus:  milliammeter   (10  to 
R    rl    r2  n+r2 

150  milliamp.),  resistance  box,  1  to  50-ohm  fixed  resistor,  1  dry  cell 
of  measured  voltage.  Measure  R  of  two  resistors  (say  70  and  50), 
(a)  when  they  are  connected  in  parallel,  and  (b)  when  they  are 
connected  in  series.  Correct  for  resistance  of  milliammeter  Ra,  thus 

E 
R=j—Ra 

Compare  with  values  given  by  formula 

-29.1,  etc. 

Try  similarly  50,  70  and  100  in  series  and  parallel. 

(b)  Cells  in  Parallel. — To  show  that  polarization  is  reduced  (with 
moderate  current)  put  3  ordinary  dry  cells  in  parallel.  Put  the 
battery  in  a  15-ohm  circuit,  with  an  ammeter,  and  repeat  with  1 
cell  of  the  same  sort. 

Experiment  6.  Polarization  and  Recovery  of  Dry  Batteries. — Use 
small  batteries,  S.  C.  type  BA-3,  3  cells  each.  In  circuit  with  re- 
sistance 30  ohms  for  6  minutes  take  open  circuit  voltage  at  start  and 
at  end  of  each  2  minutes.  Similarly  with  20  ohms,  10  and  5  in  suc- 
cession. Test  recovery  with  voltmeter  each  10  minutes  as  long  as 
convenient. 

Experiment  7.  Storage  Battery  Curves  for  Charge  and  Discharge. — 
Make  tests  with  4- volt  battery  used  for  filament  lighting  if  available. 

(a)  Charging. — Read  charging  current  and  voltage  between  ter- 
minals of  battery  at  regular  intervals,  recording  voltage,  current  and 
time.  With  each  set  of  readings  the  charging  circuit  should  be  open 
long  enough  to  read  the  open  circuit  voltage  of  the  battery.  Calcu- 
late the  apparent  internal  resistance  of  the  battery  for  each  reading. 
Measure  the  specific  gravity  of  the  electrolyte  by  means  of  a 


344  RADIO    COMMUNICATION. 

hydrometer  at  regular  intervals  during  the  charge  and  plot  a 
curve  showing  the  change  with  time  on  charge. 

(b)  Discharging. — Take  similar  readings  at  frequent  intervals  at 
the  start  and  not  so  frequently  later.  Present  results  in  curves 
with  time  as  abscissas. 

Experiment  8.  Test  of  Motor-Generator  Set  or  Dynamotor. — (a)  Use 
the  type  DM-1  dynamotor.  This  is  run  by  a  10- volt  storage  battery 
and  supplies  d.c.  current  at  300  volts.  Head  input  volts  and  am- 
peres, and  generator  volts  and  milliamperes,  when  external  resistance 
(which  is  large)  is  so  regulated  as  to  give  about  eight  current  values 
well  spaced  between  0  and  160  milliamp.  Calculate  generator 
watts  and  efficiency  for  each  output  of  current  read. 

(b)  Study  connections  and  make  diagram  of  generator  of  radio 
pack  set. 

Experiment  9.  Reactance  and  Impedance. — (a)  Given  a  coil  of 
about  10  ohms  and  0.2  henry  (spool  3000  turns  No.  16  wire,  coil  8.5  in. 
long,  2  in.  internal,  5  in.  external  diam.),  connect  it  to  a  60-cycle, 
110-v.  a.  c.  line  and  measure  current  with  an  a.c.  ammeter.  Calcu- 
late impedance. 

(b)  With  Wheatstone  bridge  measure  direct  current  resistance. 

(c)  From     formula,     Impedance =*\/R2-}-(2irfLy2)     calculate    the 
value  of  the  reactance  and  of  L. 

(d)  Attach  a  generator  like  that  of  the  pack  set  to  above  coil  and 
measure  current  and  voltage.     Taking  value  of  L  found  in  (c),  cal- 
culate value  of /for  this  machine. 

Experiment  10.  Wavemeter. — (a)  Measurement  of  an  Unknown 
Wave  Length. — Portable  wavemeter,  hot  wire  ammeter  indicator  in 
coupled  circuit,  or  crystal  detector  and  telephones.  Suitable  un- 
known circuits,  antenna  excited  oscillating  circuit  supplied  by 
pliotron. 

(b)  Wavemeter  as  Source  of  Known  Wave  Length. — Set  condenser 
of  wavemeter  to  a  chosen  wave  length,  and  excite  wavemeter  cir- 
cuit by  means  of  a  buzzer.     Tune  a  series  circuit  containing  an 
inductance  coil  and  a   condenser  (one   of  them  variable)  to  the 
wavemeter  frequency,  coupling  an  untuned  hot  wire  ammeter  circuit 
(or  crystal  detector  and  telephone)  to  the  circuit  to  be  tuned. 

(c)  Resonance  Curve. — Arrangement  in  (b)  with  hot  wire  amme- 
ter or  crystal  and  galvanometer  can  be  used.     Observe  deflections 
of  the  indicator  with  different  settings  of  the  condenser  (or  coil)  in 


RADIO    COMMUNICATION.  345 

the  circuit  to  be  tuned  to  resonance,  the  wavemeter  serving  as  a 
source  of  constant  frequency  during  the  measurements.  Plot  the 
readings  of  the  current  indicator  as  ordinates  and  the  setting  of  the 
condenser  or  inductor  as  abcissas. 

Experiment  11.  Measurement  of  Inductance  and  Capacitance  Using 
a  Wavemeter. — (a)  Measurement  of  Capacitance. — With  a  known  va- 
riable condenser  as  a  standard,  join  the  unknown  condenser  in  series 
with  an  inductance  coil,  the  circuit  being  provided  with  an  indicator 
to  show  resonance.  Couple  to  a  wavemeter  circuit  excited  by  a 
vacuum  tube.  Vary  the  frequency  of  the  exciter  until  the  indicator 
shows  that  the  unknown  circuit  is  in  resonance.  Replace  the  un- 
known condenser  by  the  known,  and  keeping  the  exciting  fre- 
quency unchanged,  vary  the  known  variable  condenser  until  the 
circuit  is  again  in  resonance  with  the  exciting  circuit.  The  un- 
known capacitance  is  equal  to  the  value  of  the  known  which  has 
replaced  it.  Suitable  unknown: — variable  air  condenser,  or  ca- 
pacitance of  an  antenna. 

(b)  Measurement   of  Inductance. — Exactly    the   same    procedure 
may  be  used  as  for  an  unknown  capacitance,  provided  a  known 
variable  inductance  coil  is  available. 

(c)  Use  of  a  Calibrated  Wavemeter  as  an  Exciter. — Either  induc- 
tance and  capacitance  may  be  measured,  provided  a  standard  of 
inductance  or  capacitance  is  available.    When  the  test  circuit  is 
in  resonance,  the  product  of  its  inductance  and  capacitance  may  be 
calculated  from  the  wave  length  indicated  by  the  wavemeter. 
Either  the  inductance  or  capacitance  of  the  test  circuit  will  be 
known,  or  can  be  derived  by  measurements  of  the  same  kind,  start- 
ing from  the  standard. 

Experiment  12.  Calibration  of  a  Receiving  Set,  Using  a  Wave- 
meter. — Excite  a  wavemeter  by  a  buzzer.  Couple  the  wavemeter 
to  the  inductance  coil  of  the  receiving  set.  With  the  inductance 
coil  and  condenser  of  the  receiving  set  at  any  desired  settings,  vary 
the  wave  length  emitted  by  the  wavemeter  until  the  sound  is  a 
maximum  in  the  telephone  of  the  receiving  set.  The  reading  of 
the  wavemeter  indicates  the  wave  length  for  which  the  set  is  ad- 
justed, with  the  inductance  and  condenser  settings  in  question. 

Or,  the  wavemeter  may  be  adjusted  to  a  chosen  wave  length, 
and  the  combination  of  inductance,  capacitance  and  coupling 
determined  by  experiment,  which  give  the  loudest  sound  in  the 
telephone  for  this  wave  length.  A  record  of  the  results  of  such 


34G  RADIO    COMMUNICATION. 

an  experiment  will  make  it  possible  for  the  operator  to  adjust  the 
apparatus  quickly  to  receive  signals  of  a  desired  wave  length. 

Experiment  13.  Effect  of  Resistance  on  Resonance  Curves.— Make 
measurements  for  obtaining  the  form  of  the  resonance  curve  of  a 
circuit  as  in  Experiment  10.  Add  a  known  resistance  of  a  few 
ohms  and  obtain  a  second  resonance  curve.  Increase  the  resistance 
again  by  the  same  amount  and  map  out  a  third  resonance  curve. 
From  the  values  of  the  maximum  currents  in  the  three  curves,  and 
the  values  of  the  inserted  resistances  determine  the  total  resistance 
in  the  three  cases.  Calculate  the  impedances  from  the  known 
inductance,  capacitance  and  resistance  at  several  points  on  each 
curve,  and  check  the  observed  currents  at  those  points. 

Experiment  14.  Inductive  Coupling. — (a)  Use  a  wavemeter  to  map 
a  curve  showing  the  relation  between  current  and  wave  length  in 
an  oscillating  circuit  which  is  closely  coupled  to  a  spark  source. 
The  source  and  oscillating  circuit  should  preferably  be  separately 
tuned  to  the  same  frequency.  Carry  the  curve  through  a  great 
enough  range  of  wave  lengths  to  show  the  double  hump  curve. 
Loosen  the  coupling  and  repeat.  The  humps  should  be  nearer 
together.  By  taking  a  third  resonance  curve  with  very  loose 
coupling  a  single  hump  may  be  obtained. 

(b)  Make  similar  measurements  with  the  same  circuit  coupled 
to  a  quenched  gap  source,  both  with  close  coupling  and  loose  cou- 
pling. 

(c)  Measure  the  coefficient  of  coupling  in  any  one  of  these  cases. 
To  do  this  measure  as  in  Experiment  11,  the  following:  (1)  the 
inductances  of  each  of  the  coupled  coils  giving  values  Z^  and  Z/2; 
(2)  the  inductance  of  the  two  coils  joined  in  series,  giving  L'\  (3)  the 
inductance  of  the  two  coils  in  series  with  the  connections  of  one 
reversed,  giving  L" .     Then  if  //  is  the  larger  value,  the  mutual 

inductance  Mis  given  by  M= — and  the  coefficient  of  coupling 

is    *=       * 


Experiment  15.  Measurement  of  Decrement.— The  circuit  whose 
decrement  is  to  be  measured  is  excited  by  a  vacuum  tube  or  some 
damped  source  of  known  decrement.  The  capacitance  of  the  circuit 
is  varied  until  the  circuit  is  in  resonance  as  shown  by  its  current 
indicator,  which  should  give  readings  proportional  to  the  current 
squared.  Having  read  the  capacitance  for  resonance,  increase  it  or 


RADIO    COM  M  UNI  CATION.  347 

decrease  it  until  the  current  squared  is  only  one  half  of  its  maximum 
value  and  again  read  the  capacitance.  The  sum  of  the  decrements 
of  the  unknown  circuit  and  the  source  may  then  be  calculated.  If  a 
vacuum  tube  source  is  used  its  decrement  is  zero.  If  a  decremeter 
is  available,  use  it  to  measure  the  decrement  of  a  transmitting  an- 
tenna. Note  the  effect  of  adding  resistance  to  the  circuit,  and  of 
adding  inductance,  re  tuning  of  course  in  the  latter  case.  For 
methods  of  calculation  and  additional  information  see  C.  74,  pp.  180 
to  199.  Check  the  decrement  of  a  circuit  here  measured  by  the 
method  of  Experiment  16,  calculating  decrement  from  the  resistance, 
capacitance,  and  inductance  of  the  circuit. 

Experiment  16.  High  Frequency  Resistance  of  Conductors. — The 
wire  or  coil  whose  resistance  is  to  be  measured  is  made  part  of  a 
resonant  circuit,  which  includes  a  thermoelement  and  galvanometer 
to  measure  relative  values  of  the  square  of  the  current.  The  circuit 
is  excited  by  coupling  to  a  vacuum  tube  source,  and  the  capacitance 
or  inductance  adjusted  until  the  thermoelement  shows  a  maximum 
current,  which  is  recorded.  A  known  resistance  is  then  added,  and 
the  maximum  current  again  noted.  The  total  resistance  of  the  cir- 
cuit is  then  calculated .  Similar  measurements  of  the  total  resistance 
are  made  with  the  unknown  resistance  removed,  the  circuit  being 
retuned  to  give  maximum  current.  The  resistance  of  the  unknown 
is  obtained  by  subtraction.  The  wave  length  of  the  source  may  be 
obtained  by  a  wavemeter.  The  direct  current  resistance  of  the 
unknown  should  be  measured  with  a  Wheatstone  bridge. 

Measure  the  resistance  of  the  unknown  at  several  wave  lengths, 
and  calculate  the  resistance  ratios  (See  C.  74,  Sec.  74).  Plot  the 
resistance  ratio  as  ordinates,  and  the  reciprocal  of  the  wave  length 


Suitable  objects  for  test:  copper  wire,  single  layer  coil,  piece  of 
metal  strip,  antenna.  Extension  of  experiment:  measure  a  resist- 
ance by  the  method  of  Experiment  15. 

Experiment  17.  Study  of  Rectifiers. — (a)  Arrange  a  voltage  divider 
in  the  circuit  of  a  steady  battery,  with  a  voltmeter  to  measure  the 
voltage  taken  off  to  a  circuit  which  includes  a  crystal  rectifier  in 
series  with  a  galvanometer  or  other  instrument  capable  of  detecting 
currents  of  a  few  microamperes.  A  reversing  switch  may  be  em- 
ployed to  reverse  the  direction  of  the  current  through  the  crystal. 
Measure  the  current  through  the  crystal  for  each  direction  of  the 
voltage  and  for  a  number  of  values  of  voltage  up  to  20  volts.  Measure 
the  currents  for  the  same  values  of  alternating  voltages  of  60  cycles. 


348  RADIO    COMMUNICATION. 

(b)  Make  similar  tests  with  a  Fleming  valve.     Note  which  way 
the  current  flows  through  the  tube  and  compare  with  theory. 

(c)  Examine  and  trace  out  the  connections  of  a  tungar  rectifier. 
Measure  the  current  and  voltage  on  the  a.c.  end  and  the  current  and 
voltage  on  the  d.c.  end.     Note  how  the  alternating  current  varies 
as  the  direct  current  load  is  varied. 

Experiment  18.  Characteristic  Curves  of  Type  VT-1  Tube  with 
Constant  Filament  Current. — Connect  up  the  tube  with  a  rheo.-tat 
and  ammeter  in  the  filament  circuit,  so  that  the  filament  current 
may  be  adjusted  to  its  normal  value  and  held  constant.  Arrange  a 
battery  of  5  to  10  volts  with  a  voltage  divider  so  connected  that  the 
grid  voltage  may  be  made  positive  or  negative  with  respect  to  the 
fdament.  The  voltage  divider  allows  its  value  to  be  adjusted  in 
small  steps.  The  plate  battery  should  consist  of  a  sufficient  number 
of  cells  to  permit  the  operation  of  the  tube  under  normal  working 
conditions.  A  suitable  low  reading  milliammeter  or  calibrated 
galvanometer  should  be  included  in  the  plate  circuit.  The  grid 
circuit  will  require  a  galvanometer  to  read  the  small  grid  current. 
A  low  reading  voltmeter  will  be  necessary  to  measure  the  grid  voltage. 

Adjust  the  plate  voltage  to  the  normal  value  for  the  tube  in  ques- 
tion and,  keeping  it  constant,  vary  the  grid  voltage  in  steps,  recording 
for  each  setting  the  plate  and  grid  currents  and  plate  voltage.  Plot 
the  plate  current  as  ordinates  with  grid  voltages  as  abscissas.  Make 
a  second  curve  with  grid  currents  as  ordinates  and  grid  voltages  as 


Obtain  similar  characteristic  curves  with  the  plate  voltage  ad- 
justed to  other  values  lower  than  the  normal  voltage. 

Experiment  19.  Characteristic  Curves  of  Type  VT-1  Tube  as 
Changed  by  a  Signal.— Arrange  a  circuit  containing  a  coil,  a  key, 
and  sufficient  resistance  so  that  the  current  which  will  flow  when 
connection  is  made  to  a  60-cycle,  110-volt  line  will  be  only  a  few 
tenths  of  an  ampere.  The  apparatus  used  in  the  previous  experi- 
ment is  also  to  be  changed  only  to  the  extent  of  including  an  induct- 
ance in  the  grid  circuit. 

Bring  up  the  coil  which  is  carrying  the  60-cycle  current,  from  a 
distance  until  the  coupling  is  sufficient  to  cause  a  moderate  change 
in  the  plate  and  grid  circuits.  Adjusting  the  grid  voltage  to  differ- 
ent values,  observe  the  plate  and  grid  currents,  both  when  the  key 
is  open  and  when  it  is  closed.  Plot  in  two  curves  the  changes  in 
plate  current  and  grid  current  as  ordinates  against  grid  voltages  as 


RADIO   COMMUNICATION.  349 

abscissas.  Draw  conclusions  as  to  the  most  suitable  values  of  grid 
voltage,  in  order  that  such  signals  may  produce  the  greatest  changes 
in  the  plate  current,  and  in  order  that  the  tube  may  be  a  good  rectifier. 

Experiment  20.  Type  VT-2  Tube  as  Source  of  Oscillations. — Con- 
nect the  tube  as  in  Fig.  262  with  a  hot  wire  ammeter  in  the  oscillation 
circuit,  and  with  a  given  setting  of  the  condenser  in  the  oscillation 
circuit,  vary  the  coupling  until  the  ammeter  indicates  the  maximum 
current.  Record  this,  and  measure  the  wave  length  of  the  oscilla- 
tions by  means  of  a  wavemeter.  Adjust  the  circuit  to  other  wave 
lengths,  recording  the  maximum  current  which  can  be  obtained 
in  each  case.  Make  similar  tests  with  the  other  schemes  of  con- 
nection in  C.  74,  Figs.  147  and  148. 

Experiment  21.  Heterodyne  Reception. — Arrange  a  vacuum  tube 
circuit  to  act  as  a  transmitter  of  oscillations.  These  oscillations  are 
to  be  received  in  a  second  circuit  in  which  independent  oscillations 
may  be  produced.  The  latter  circuit  may  be  that  of  an  oscillating 
vacuum  tube,  connected  as  in  C.  74,  Fig.  145.  The  receiving  cir- 
cuit and  the  circuit  which  is  transmitting  signals  should  be  tuned 
to  the  same  frequency  by  a  preliminary  test  with  a  wavemeter. 
Start  the  receiving  tube  to  oscillate  and  then  increase  the  coupling 
to  the  source  of  signals.  Vary  the  inductance  or  capacitance  in  the 
receiving  circuit  a  very  little.  The  pitch  of  the  note  received  in  the 
telephones  should  be  very  sensitive  to  the  smallest  change  of  induct- 
ance or  capacitance,  and  it  should  be  easy  to  make  it  pass  from  the 
lowest  to  the  highest  audible  frequency.  Try  to  adjust  the  receiving 
circuit  without  the  preliminary  tuning  of  the  transmitting  and 
receiving  circuits. 


APPENDIX  2. 

UNITS. 

Every  measurement  must  be  expressed  in  terms  of  two  factors. 
One  of  these  is  a  definite  amount  of  the  thing  measured,  called  the 
unit;  the  other  is  a  mere  number,  being  the  number  of  times  the  unit 
is  taken.  Thus  we  speak  of  a  certain  action  taking  place  in  15  sec- 
onds. The  second  is  the  unit  in  which  the  time  specified  is  measured . 
A  standard  is  a  different  thing  from  a  unit;  it  is  the  representation 
of  a  unit.  It  is  necessary  that  there  be  authoritative  standards 
representing  certain  units.  When  a  length  is  measured  by  a  number 
of  different  measuring  sticks,  differences  in  the  results  can  some- 
times be  detected.  The  true  length  would  be  given  by  comparison 
with  some  one  measuring  stick  that  had  been  agreed  upon  as  the 
standard.  The  standards  representing  various  units,  for  the  use 
of  the  United  States,  are  kept  at  the  Bureau  of  Standards  in  Wash- 
ington. Measurements  are  frequently  made  in  ordinary  work 
without  any  reference  to  the  existence  of  a  standard.  A  standard 
can  be  destroyed  and  the  unit  still  be  used  as  before.  While  in 
many  measuring  processes  standards  are  actually  used  (as  for  ex- 
ample, in  weighing  on  a  balance,  the  weights  used  on  one  side  are 
actually  standards),  in  many  other  measuring  processes  standards 
are  not  used,  but  instead  marks  upon  a  measuring  instrument 
enable  one  to  express  the  measurement  in  terms  of  units.  Thus,  a 
voltmeter  is  a  means  of  measuring  voltage,  and  the  resulting  measure- 
ments are  expressed  in  terms  of  a  unit  called  the  volt. 

Electrical  units  are  based  upon  the  units  of  the  metric  system, 
which  is  the  name  given  to  the  system  of  units  used  on  the  Con- 
tinent of  Europe ;  it  is  a  much  simpler  system  than  the  English  and 
American  systems  of  units.  The  fundamental  units  in  the  metric 
system  are  the  meter,  the  gram,  and  the  second.  The  "meter"  is 
defined  as  the  length  of  a  certain  metal  standard  bar  which  is  pre- 
served at  an  international  bureau  near  Paris.  The  "gram"  is  a 
thousandth  part  of  a  certain  mass  of  metal  kept  as  a  standard  of 
350 


RADIO    COMMUNICATION. 


351 


mass  at  the  same  place.  Each  Government  has  copies  of  these 
two  fundamental  standards.  The  "second"  is  the  familiar  unit 
of  time. 

These  units  are  comparatively  familiar  to  the  radio  man.  Thus 
the  meter  is  universally  used  for  the  expression  of  the  length  of  radio 
waves.  The  meter  is  a  little  more  than  one  yard  in  length.  The 
gram  is  not  far  from  one-thirtieth  of  an  ounce.  The  relations  be- 
tween these  units  and  the  American  and  English  units  is  given 
approximately  in  the  following: 

1  inch =2. 540  centimeters =2 5. 40  millimeters 

1  foot=30.48  centimeters=0.3048  meter 

1  yard =9 1.44  centimeters =0.9 144  meter 

1  mile =1.609  kilometers =1609  meters 

1  ounce  (avoirdupois) =28. 35  grams 

1  pound=0.4536  kilogram =453. 6  grams 

1  liquid  quart=0.9463  liter 

]  dry  quart =1.101  liters 

1  millimeter=0.03937  inch 

1  centimeter=0.3937  inch 

1  meter =3. 281  feet= 1.094  yards 

1  kilometer=0.6214  mile 

1  gram=15.43  grains=0.  03527  ounce  (avoirdupois) 

1  kilogram=2.205  pounds 

1  liter=1.057  liquid  quarts=0.2642  gallon 

1  hectoliter=90.81  dry  quarts=2.838  bushels 

In  connection  with  the  units  of  the  metric  system,  certain  pre- 
fixes are  used  to  indicate  smaller  or  larger  units.  (Thus  the  word 
' '  centi ' '  is  used  to  designate  100th  part.)  These  prefixes  are  shown 
in  the  following  list  with  their  abbreviations: 


Prefix 

Abbreviation 

Meaning. 

micro 

One  millionth 

milli 

m 

One  thousandth 

centi 

c 

One  hundredth 

deci 

d 

One  tenth 

deka 

dk 

Ten 

hekto 

h 

One  hundred 

kilo 

k 

One  thousand 

mega 

M 

One  million 

352  RADIO    COMMUNICATION. 

Without  giving  any  historical  information  as  to  the  development 
of  electric  and  magnetic  units,  it  may  be  said  that  those  now  used 
are  the  so-called  international  electric  units.  The  international 
units  are  based  on  four  fundamental  units,  the  ohm,  ampere,  centi- 
meter, and  second.  The  first  of  these  is  the  unit  of  resistance, 
and  is  defined  in  terms  of  the  resistance  of  a  very  pure  conductor 
of  specified  dimensions.  The  ampere  is  the  unit  of  current  and  is 
defined  in  terms  of  a  chemical  effect  of  electric  current,  the  amount 
of  silver  deposited  from  a  certain  solution  for  a  current  flow  for 
a  definite  time.  The  other  electric  units  follow  from  these  in  ac- 
cordance with  the  principles  of  electrical  science.  Some  of  the 
units  thus  defined  are  given  in  the  following  definitions  which  are 
those  adopted  by  international  congresses  of  science,  and  universally 
used  in  electrical  work. 

The  ' '  ohm  "  is  the  resistance  of  a  thread  of  mercury  at  the  tempera- 
ture of  melting  ice,  14.4521  grams  in  mass,  of  uniform  cross  section, 
and  a  length  of  106.300  centimeters. 

The  "ampere"  is  the  current  which  when  passed  through  a  solu- 
tion of  nitrate  of  silver  in  water  in  accordance  with  certain  specifi- 
cations, deposits  silver  at  the  rate  of  0.00111800  of  a  gram  per  second. 

The  "volt"  is  the  electromotive  force  which  produces  a  current  of 
one  ampere  when  steadily  applied  to  a  conductor  the  resistance  of 
which  is  one  ohm. 

The  "coulomb"  is  the  quantity  of  electricity  transferred  by  a  cur- 
rent of  one  ampere  in  one  second. 

The  ' '  farad  "  is  the  capacitance  of  a  condenser  in  which  a  potential 
difference  of  one  volt  causes  it  to  have  a  charge  of  one  coulomb  of 
electricity. 

The  ' '  henry  "  is  the  inductance  in  a  circuit  in  which  the  electromo- 
tive force  induced  is  one  volt  when  the  inducing  current  varies  at 
the  rate  of  one  ampere  per  second. 

The  "watt "  is  the  power  expended  by  a  current  of  one  ampere  in  a 
resistance  of  one  ohm. 

The  "joule"  is  the  energy  expended  in  one  second  by  a  flow  of 
one  ampere  in  one  ohm. 

The  watt  and  joule  are  not  primarily  electric  units,  but  they 
need  to  b^  learned  in  connection  with  electric  units  because  the 
energy  required  or  the  power  expended  in  electrical  processes  are 
among  the  most  important  phases  of  the  actions.  Another  unit  of 


RADIO   COMMUNICATION. 


353 


quantity  of  electricity-,  in  addition  to  the  coulomb,  is  the  "ampere- 
hour,"  which  is  the  quantity  of  electricity  transferred  by  a  current 
of  one  ampere  in  one  hour.  The  units  of  capacitance  actually  used 
in  radio  work  are  the  "microfarad"  and  the  "  micromicrof  arad  " 
(a  millionth  of  a  millionth  of  a  farad),  and  not  the  farad,  which  is  too 
large  a  unit.  The  units  of  inductance  used  are  the  "microhenry'1 
and  the  "millihenry." 

For  further  information  on  electric  and  magnetic  units  see  Cir- 
cular of  the  Bureau  of  Standards  No.  60,  "Electric  Units  and  Stand- 
ards," which,  like  all  other  publications  of  that  Bureau,  may  be 
obtained  upon  written  application. 


ABBREVIATIONS  OF  UNITS. 


Unit. 


Abbreviation. 


amperes  .............  amp. 

ampere-hours  .........  amp-hr. 

centimeters  ..........  cm. 

centhneter-gram-sec- 
ond  ................  cgs. 

cubic  centimeters  ____  cm3 

cubic  inches  ..........  cu.  in. 

cycles  per  second  .....  ~ 

degrees  Centigrade  ____  °  C 

degrees  Fahrenheit.  .  .°  F 
feet  ..................  ft. 

foot-pounds  ..........  ft-lb. 

grams  ...............  g. 

henries  ...............  h. 

inches  ................  in. 

kilograms  .............  kg. 

97340°—  19  -  23 


Unit.  Abbreviation 

kilometers km. 

kilowatts kw. 

kilo  watt-ho  ui  s kw-hr. 

kilovolt-amperes .leva. 

meters rn. 

microfarads mfd. 

micro  microfarads ....  inicro-mf  d . 

millihenries mh. 

millimeters mm. 

pounds lb. 

seconds sec. 

square  centimeters cm2 

square  inches sq.  in. 

volts... v. 

watts...  ..w. 


APPENDIX  3. 


SYMBOLS  USED  FOR  PHYSICAL  QUANTITIES. 


Physical  Quantity.          Symbol. 

area S  or  A 

base    of    napieriau    loga- 
rithms =2. 71 8 e 

capacitance C 

coupling  coefficient k 

current,  instantaneous 

value i 

current,  effective  value. . .  I 

decrement 5 

density d 

dielectric  constant K 

electric  field  intensity £, 

electromotive     force,     in- 
stantaneous value c 

electromotive  force,  effec- 
tive value E 

energy W 

force F 

frequency f 

frequency  X2x co 

gravity,  acceleration  of ...  g 

height h 

impedance Z 

inductance,  self L 

length 1 

magnetic  field  intensity . . .  H 
354 


Physical  Quantity.  Symbol. 

magnetic  flux <£ 

magnetic  induction B 

mass m 

mutual  inductance M 

number  of  revolutions n 

period  of  a  complete  oscil- 
lation    T 

permeability M 

phase  angle O 

phase  difference ^ 

potential  difference V 

power,  instantaneous 

value p 

power,  average  value P 

quantity  of  electricity Q 

ratio  circumference  of  cir- 
cle to  diameter =3. 1416.  TT 

reactance 

resistance Pv 

temperature  coefficient  —  « 

time t 

velocity v 

velocity  of  light c 

wave  length -  X 

wave  length  in  meters Xm 

work . .                           ....  W 


RADIO    COMMITS  I  CATION. 


355 


A  Iternator  -  -  ..-  /Cjf^-(f\h-  Variable  Inductor  - 

Ammeter (J) Key 

Antenna LU  Resistor. 

Arc £  Variable  resistor. 

— umiih  5witch  5P5T 

— ^HRF[L_  «         5.  ROT. 

Variable  Condenser.—^— 

Connection  of  wires 1  .           D.PD.T. _~ 

Wo    Connec-tlon- A.  • 

Coi !?  _  _  _TS  &  Tele b hone   receiver.  _7T~or  ^^ 

TelejiKone  trarv^mitter nQ^ 

Defector — lg Thermoelement U 

/<T\  T       /                 -EF 

nome.Ter ~~~(Cj   ) IrAnsiormep c3 

^lA.n m-9 Vacuum    tube- 


C)  round  : 

Inductor 


o 


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